Pub Date : 2026-03-15Epub Date: 2025-12-08DOI: 10.1016/j.jfa.2025.111299
Xu Zhang , Ying Zhang , Rui Zhu
<div><div>We are concerned with clustering-peak solutions to the following stationary Hamiltonian elliptic system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>v</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mspace></mspace><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mi>v</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mspace></mspace><mrow><mi>as</mi></mrow><mspace></mspace><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> Here <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is a small parameter, <em>V</em> has a local maximum point, and <span><math><mi>f</mi><mo>,</mo><mi>g</mi></math></span> are assumed to be of critical growth in the sense of the Trudinger–Moser inequality. Differently from most results that consider solutions for the critical equation near the ground state level <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, we attempt to construct high-energy solutions at levels close to <span><math><mi>k</mi><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> for any integer <em>k</em>. The solutions possess <em>k</em> peaks that cluster around a local maximum of <em>V</em> as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>. Due to the critical growth of the nonlinear terms, in order to handle the compactness problem, we make uniform estimates of the exponential integral of functions in a suitable neighborhood. Since there is no non-degeneracy property for the ground state solutions of the limit system, the variational method is applied here, and a sensitive lower gradient estimate should be made when the local centroids of the functions are away from the local maximum of <em>V</em>. We introduce a new method to obtain this estimate, which differs from the ideas of Del Pino and Felmer (2002) <span><span>[27]</span></span>, and Byeon and Tanaka (2013, 2014) <span><span>[9]</span></span>, <span><span>[10]</span></span>. In addition, the fact that the energy functional corresponding to Hamiltonian elliptic systems is strongly indefinite poses additional difficulties for
我们关注以下平稳哈密顿椭圆系统{−ε2Δu+V(x)u=g(V)inR2,−ε2Δv+V(x) V =f(u)inR2,u(x)→0，V(x)→0as|x|→∞的聚类峰解。这里ε>；0是一个小参数，V有一个局部极大点，f，g在Trudinger-Moser不等式意义上被假定为临界增长。与大多数考虑临界方程在基态能级c0附近的解的结果不同，我们试图在接近kc0的能级上构造任意整数k的高能解。解具有k个峰，这些峰聚集在V的局部最大值ε→0附近。由于非线性项的临界增长，为了处理紧性问题，我们在合适的邻域内对函数的指数积分作了一致估计。由于极限系统的基态解不具有非简并性，本文采用变分方法，当函数的局部质心远离v的局部最大值时，需要进行敏感的低梯度估计。本文引入了一种不同于Del Pino and Felmer(2002)[27]和Byeon and Tanaka(2013, 2014)[9]，[10]的新方法来获得这种估计。此外，哈密顿椭圆系统对应的能量泛函是强不定的，这给我们的证明带来了额外的困难。通过考虑外部区域上的辅助极大极小问题和对初始路径能量的精确估计，得到了该泛函在合适邻域内的连接结构。结合前面提到的梯度估计和应用局部变形的方法，我们得到了系统期望解的存在性。
{"title":"Clustering type solutions for critical elliptic system in dimension two","authors":"Xu Zhang , Ying Zhang , Rui Zhu","doi":"10.1016/j.jfa.2025.111299","DOIUrl":"10.1016/j.jfa.2025.111299","url":null,"abstract":"<div><div>We are concerned with clustering-peak solutions to the following stationary Hamiltonian elliptic system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>v</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mspace></mspace><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mi>v</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mspace></mspace><mrow><mi>as</mi></mrow><mspace></mspace><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> Here <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is a small parameter, <em>V</em> has a local maximum point, and <span><math><mi>f</mi><mo>,</mo><mi>g</mi></math></span> are assumed to be of critical growth in the sense of the Trudinger–Moser inequality. Differently from most results that consider solutions for the critical equation near the ground state level <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, we attempt to construct high-energy solutions at levels close to <span><math><mi>k</mi><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> for any integer <em>k</em>. The solutions possess <em>k</em> peaks that cluster around a local maximum of <em>V</em> as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>. Due to the critical growth of the nonlinear terms, in order to handle the compactness problem, we make uniform estimates of the exponential integral of functions in a suitable neighborhood. Since there is no non-degeneracy property for the ground state solutions of the limit system, the variational method is applied here, and a sensitive lower gradient estimate should be made when the local centroids of the functions are away from the local maximum of <em>V</em>. We introduce a new method to obtain this estimate, which differs from the ideas of Del Pino and Felmer (2002) <span><span>[27]</span></span>, and Byeon and Tanaka (2013, 2014) <span><span>[9]</span></span>, <span><span>[10]</span></span>. In addition, the fact that the energy functional corresponding to Hamiltonian elliptic systems is strongly indefinite poses additional difficulties for ","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111299"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-11DOI: 10.1016/j.jfa.2025.111275
Yilin Song , Ruixiao Zhang , Jiqiang Zheng
In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schrödinger equation with harmonic potential in dimensions ,(PNLS) where . Motivated by Planchon et al. (2023) [34], we first establish the bilinear Strichartz estimates, which removes the ε-loss of Burq et al. (2025) [7]. To show the polynomial growth of Sobolev norm, our proof relies on the upside-down I-method associated to the harmonic oscillator. Due to the lack of Fourier transform or expansion, we need to carefully control the frequency interaction of the type “high-high-low-low”. To overcome this difficulty, we establish the explicit interaction for products of eigenfunctions. Our bound recovers the result of Planchon et al. (2023) [34] in dimension two and is new in dimension three.
在本文中，我们研究了在维数d=2,3,(PNLS){i∂tu−Hu=|u|2u,(t,x)∈R×Rd,u(0,x)=u0(x)，其中H= - Δ+|x|2中具有谐波势的散焦三次非线性Schrödinger方程解的高阶Sobolev范数的增长。受Planchon et al. (2023) b[34]的启发，我们首先建立了双线性Strichartz估计，该估计消除了Burq et al. (2025) b[7]的ε-损失。为了证明Sobolev范数的多项式增长，我们的证明依赖于与谐振子相关的倒i方法。由于缺乏傅里叶变换或展开，我们需要仔细控制“高-高-低-低”型的频率相互作用。为了克服这一困难，我们建立了特征函数积的显式相互作用。我们的边界恢复了Planchon et al.(2023)[34]在二维上的结果，并且在三维上是新的。
{"title":"On growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions d = 2,3","authors":"Yilin Song , Ruixiao Zhang , Jiqiang Zheng","doi":"10.1016/j.jfa.2025.111275","DOIUrl":"10.1016/j.jfa.2025.111275","url":null,"abstract":"<div><div>In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schrödinger equation with harmonic potential in dimensions <span><math><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>,<span><span><span>(PNLS)</span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>−</mo><mi>H</mi><mi>u</mi><mo>=</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>∈</mo><mi>R</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> where <span><math><mi>H</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Motivated by Planchon et al. (2023) <span><span>[34]</span></span>, we first establish the bilinear Strichartz estimates, which removes the <em>ε</em>-loss of Burq et al. (2025) <span><span>[7]</span></span>. To show the polynomial growth of Sobolev norm, our proof relies on the upside-down <em>I</em>-method associated to the harmonic oscillator. Due to the lack of Fourier transform or expansion, we need to carefully control the frequency interaction of the type “high-high-low-low”. To overcome this difficulty, we establish the explicit interaction for products of eigenfunctions. Our bound recovers the result of Planchon et al. (2023) <span><span>[34]</span></span> in dimension two and is new in dimension three.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111275"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the local, iterative Lie Schwinger block-diagonalization method which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps, for which we provide an explicit formula. This improves earlier results concerning the persistence of the so-called bulk gap in these models, besides illustrating the power of our general methods in a non-trivial application.
{"title":"Boundary effects and the stability of the low energy spectrum of the AKLT model","authors":"Simone Del Vecchio , Jürg Fröhlich , Alessandro Pizzo , Alessio Ranallo","doi":"10.1016/j.jfa.2025.111269","DOIUrl":"10.1016/j.jfa.2025.111269","url":null,"abstract":"<div><div>In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the <em>local, iterative Lie Schwinger block-diagonalization method</em> which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps, for which we provide an explicit formula. This improves earlier results concerning the persistence of the so-called <em>bulk</em> gap in these models, besides illustrating the power of our general methods in a non-trivial application.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111269"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145570768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-10DOI: 10.1016/j.jfa.2025.111270
Noé de Rancourt , Ondřej Kurka
We prove that non-Hilbertian separable Orlicz sequence spaces are ergodic, i.e., the equivalence relation Borel reduces to the isomorphism relation between subspaces of every such space. This is done by exhibiting non-Hilbertian asymptotically Hilbertian subspaces in those spaces, and appealing to a result by Anisca. In particular, each non-Hilbertian Orlicz sequence space contains continuum many pairwise non-isomorphic subspaces.
As a consequence, we prove that the twisted Hilbert spaces constructed by Kalton and Peck are either Hilbertian, or ergodic. This applies in particular to the Kalton–Peck space and all twisted Hilbert spaces generated by complex interpolation between Orlicz sequence spaces.
{"title":"The ergodicity of Orlicz sequence spaces","authors":"Noé de Rancourt , Ondřej Kurka","doi":"10.1016/j.jfa.2025.111270","DOIUrl":"10.1016/j.jfa.2025.111270","url":null,"abstract":"<div><div>We prove that non-Hilbertian separable Orlicz sequence spaces are ergodic, i.e., the equivalence relation <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> Borel reduces to the isomorphism relation between subspaces of every such space. This is done by exhibiting non-Hilbertian asymptotically Hilbertian subspaces in those spaces, and appealing to a result by Anisca. In particular, each non-Hilbertian Orlicz sequence space contains continuum many pairwise non-isomorphic subspaces.</div><div>As a consequence, we prove that the twisted Hilbert spaces <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>ϕ</mi><mo>)</mo></math></span> constructed by Kalton and Peck are either Hilbertian, or ergodic. This applies in particular to the Kalton–Peck space <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and all twisted Hilbert spaces generated by complex interpolation between Orlicz sequence spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111270"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111286
Feimin Huang , Guiqin Qiu , Yi Wang , Xiaozhou Yang
<div><div>We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>y</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi></math></span>, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, separated by a curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. This is the first result on the nonlinear time-asymptotic stability of non-self-similar rarefaction waves. Furthermore, we can get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.</div><div>The main difficulty comes from the fact that the initial discontinuity of 2D non-self-similar rarefaction wave is a curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. Fortunately, we uncover a novel property that the non-self-similar inviscid rarefaction wave is also asymptotically stable with respect to the discontinuity curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. More precisely, let <span><math><msubsup><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>R</mi></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> be the corresponding non-self-similar rarefaction wave with the initial discontinuity curve <span><math><mi>y</mi><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, then <span><math><msub><mrow><mo>‖</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>R</mi></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>R</mi></mrow></msubsup><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>≤</mo><mfrac><mrow><mi>C</mi></mrow><mrow><mi>t</mi></mrow></mfrac></math></span> if <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub></math></span> is bounded. Based on this property, we prove that the asymptotic stability of non-self-similar rarefaction wave corresponding to the general initial discontinuity <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is equivalent to that of the non-self-similar rarefaction wave with an initial discontinuity given by the modification curve
{"title":"Asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation","authors":"Feimin Huang , Guiqin Qiu , Yi Wang , Xiaozhou Yang","doi":"10.1016/j.jfa.2025.111286","DOIUrl":"10.1016/j.jfa.2025.111286","url":null,"abstract":"<div><div>We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>y</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi></math></span>, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, separated by a curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. This is the first result on the nonlinear time-asymptotic stability of non-self-similar rarefaction waves. Furthermore, we can get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.</div><div>The main difficulty comes from the fact that the initial discontinuity of 2D non-self-similar rarefaction wave is a curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. Fortunately, we uncover a novel property that the non-self-similar inviscid rarefaction wave is also asymptotically stable with respect to the discontinuity curve <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. More precisely, let <span><math><msubsup><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>R</mi></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> be the corresponding non-self-similar rarefaction wave with the initial discontinuity curve <span><math><mi>y</mi><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, then <span><math><msub><mrow><mo>‖</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>R</mi></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>R</mi></mrow></msubsup><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>≤</mo><mfrac><mrow><mi>C</mi></mrow><mrow><mi>t</mi></mrow></mfrac></math></span> if <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub></math></span> is bounded. Based on this property, we prove that the asymptotic stability of non-self-similar rarefaction wave corresponding to the general initial discontinuity <span><math><mi>y</mi><mo>=</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is equivalent to that of the non-self-similar rarefaction wave with an initial discontinuity given by the modification curve","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111286"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111285
Pritam Ganguly , Abhishek Ghosh
In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Korányi balls in the Heisenberg group. We also generalize the result to more general UMD lattices. As a key stepping stone, we establish the - boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.
{"title":"Dimension free estimates for the vector-valued Hardy–Littlewood maximal function on the Heisenberg group","authors":"Pritam Ganguly , Abhishek Ghosh","doi":"10.1016/j.jfa.2025.111285","DOIUrl":"10.1016/j.jfa.2025.111285","url":null,"abstract":"<div><div>In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Korányi balls in the Heisenberg group. We also generalize the result to more general UMD lattices. As a key stepping stone, we establish the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>- boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111285"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bilinear Fourier multipliers of the form are considered. It is proved that if is in the Hörmander class with then the corresponding bilinear operator is bounded in , , and . This improves a result given by Rodríguez-López, Rule and Staubach.
{"title":"On some bilinear Fourier multipliers with oscillating factors, I","authors":"Tomoya Kato , Akihiko Miyachi , Naoto Shida , Naohito Tomita","doi":"10.1016/j.jfa.2025.111289","DOIUrl":"10.1016/j.jfa.2025.111289","url":null,"abstract":"<div><div>Bilinear Fourier multipliers of the form <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mo>(</mo><mo>|</mo><mi>ξ</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>η</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>ξ</mi><mo>+</mo><mi>η</mi><mo>|</mo><mo>)</mo></mrow></msup><mi>σ</mi><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>η</mi><mo>)</mo></math></span> are considered. It is proved that if <span><math><mi>σ</mi><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>η</mi><mo>)</mo></math></span> is in the Hörmander class <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mi>m</mi><mo>=</mo><mo>−</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></span> then the corresponding bilinear operator is bounded in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>→</mo><mi>b</mi><mi>m</mi><mi>o</mi></math></span>, <span><math><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>×</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. This improves a result given by Rodríguez-López, Rule and Staubach.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111289"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111287
Huayou Xie , Junming Liu , Qingze Lin
In this paper, we investigate the conditions for the boundedness and compactness of the following Cesàro-type operator where μ is a positive finite Borel measure supported on , acting on two derivative-type spaces of analytic functions (i.e., derivative Hardy spaces and weighted Dirichlet spaces ). This work continues the lines of the previous works, by Lin-Xie, about weighted Bergman spaces and so forth (J. Funct. Anal., 2025). Interestingly, we find that the boundedness and compactness of acting on derivative Hardy spaces are equivalent, which behaves quite differently from the corresponding results on Hardy spaces and other analytic function spaces.
{"title":"Cesàro-type operators on derivative-type Hilbert spaces of analytic functions II","authors":"Huayou Xie , Junming Liu , Qingze Lin","doi":"10.1016/j.jfa.2025.111287","DOIUrl":"10.1016/j.jfa.2025.111287","url":null,"abstract":"<div><div>In this paper, we investigate the conditions for the boundedness and compactness of the following Cesàro-type operator<span><span><span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mrow><mo>(</mo><munder><mo>∫</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></munder><msup><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>d</mi><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>(</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <em>μ</em> is a positive finite Borel measure supported on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, acting on two derivative-type spaces of analytic functions (i.e., derivative Hardy spaces <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and weighted Dirichlet spaces <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>). This work continues the lines of the previous works, by Lin-Xie, about weighted Bergman spaces and so forth (J. Funct. Anal., 2025). Interestingly, we find that the boundedness and compactness of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> acting on derivative Hardy spaces are equivalent, which behaves quite differently from the corresponding results on Hardy spaces and other analytic function spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111287"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145570818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111284
Rui Bai , Chunrong Feng , Huaizhong Zhao
We study the small noise asymptotic for stochastic Burgers equations on with the Dirichlet boundary condition. We consider the case in which the noise is more singular than space-time white noise. We let the noise magnitude and the covariance operator converge to and prove the large deviation principle for solutions, uniformly with respect to the bounded initial value of the equation. Furthermore, we set to be a trace class operator and converge to with in a suitable way such that the invariant measures exist. Then, we prove the large deviation principle for the invariant measures of stochastic Burgers equations.
{"title":"Large deviation principle for invariant measures of stochastic Burgers equations","authors":"Rui Bai , Chunrong Feng , Huaizhong Zhao","doi":"10.1016/j.jfa.2025.111284","DOIUrl":"10.1016/j.jfa.2025.111284","url":null,"abstract":"<div><div>We study the small noise asymptotic for stochastic Burgers equations on <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> with the Dirichlet boundary condition. We consider the case in which the noise is more singular than space-time white noise. We let the noise magnitude <span><math><msqrt><mrow><mi>ϵ</mi></mrow></msqrt><mo>→</mo><mn>0</mn></math></span> and the covariance operator <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>ϵ</mi></mrow></msub></math></span> converge to <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> and prove the large deviation principle for solutions, uniformly with respect to the bounded initial value of the equation. Furthermore, we set <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>ϵ</mi></mrow></msub></math></span> to be a trace class operator and converge to <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> with <span><math><mi>α</mi><mo><</mo><mn>1</mn></math></span> in a suitable way such that the invariant measures exist. Then, we prove the large deviation principle for the invariant measures of stochastic Burgers equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111284"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111283
Marzieh Forough , Ja A. Jeong , Karen R. Strung
In this paper, we construct recursive subhomogeneous decompositions for the Cuntz–Pimsner algebras obtained from breaking the orbit of a minimal Hilbert -bimodule at a closed subset with non-empty interior. This generalizes the known recursive subhomogeneous decomposition for orbit-breaking subalgebras of crossed products by minimal homeomorphisms.
{"title":"Recursive subhomogeneity of orbit-breaking subalgebras of C⁎-algebras associated to minimal homeomorphisms twisted by line bundles","authors":"Marzieh Forough , Ja A. Jeong , Karen R. Strung","doi":"10.1016/j.jfa.2025.111283","DOIUrl":"10.1016/j.jfa.2025.111283","url":null,"abstract":"<div><div>In this paper, we construct recursive subhomogeneous decompositions for the Cuntz–Pimsner algebras obtained from breaking the orbit of a minimal Hilbert <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>-bimodule at a closed subset <span><math><mi>Y</mi><mo>⊂</mo><mi>X</mi></math></span> with non-empty interior. This generalizes the known recursive subhomogeneous decomposition for orbit-breaking subalgebras of crossed products by minimal homeomorphisms.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111283"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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