Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110854
Irina Holmes Fay , Guillermo Rey , Kristina Ana Škreb
We find the exact Bellman function associated to the level-sets of sparse operators acting on characteristic functions.
{"title":"Sharp restricted weak-type estimates for sparse operators","authors":"Irina Holmes Fay , Guillermo Rey , Kristina Ana Škreb","doi":"10.1016/j.jfa.2025.110854","DOIUrl":"10.1016/j.jfa.2025.110854","url":null,"abstract":"<div><div>We find the exact Bellman function associated to the level-sets of sparse operators acting on characteristic functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110854"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110859
Vít Musil , Luboš Pick , Jakub Takáč
We characterize when an Orlicz space is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space in terms of a balance condition involving parameters , and a Young function A. In the course of the proof, we develop a new method based on an inequality of Young type involving the measure of level sets of a given function.
{"title":"Almost compact embeddings between Orlicz and Lorentz spaces","authors":"Vít Musil , Luboš Pick , Jakub Takáč","doi":"10.1016/j.jfa.2025.110859","DOIUrl":"10.1016/j.jfa.2025.110859","url":null,"abstract":"<div><div>We characterize when an Orlicz space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup></math></span> in terms of a balance condition involving parameters <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, and a Young function <em>A</em>. In the course of the proof, we develop a new method based on an inequality of Young type involving the measure of level sets of a given function.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110859"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445539","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 : 2025-02-10DOI: 10.1016/j.jfa.2025.110866
Riccardo Adami , Jinyeop Lee
We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential. Assuming a simultaneous mean-field and short-range scaling with the short-range proceeding slower than the mean-field, and choosing an initial fully condensed state, we prove propagation of chaos and obtain an effective one-particle Schrödinger equation with a defocusing nonlinearity concentrated at a point. More precisely, we prove convergence of one-particle density operators in the trace-class topology and estimate the fluctuations as superexponential. This is the first derivation of the so-called nonlinear delta model, widely investigated in the last decades, as a phenomenological model for several physical phenomena.
{"title":"Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction","authors":"Riccardo Adami , Jinyeop Lee","doi":"10.1016/j.jfa.2025.110866","DOIUrl":"10.1016/j.jfa.2025.110866","url":null,"abstract":"<div><div>We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential. Assuming a simultaneous mean-field and short-range scaling with the short-range proceeding slower than the mean-field, and choosing an initial fully condensed state, we prove propagation of chaos and obtain an effective one-particle Schrödinger equation with a defocusing nonlinearity concentrated at a point. More precisely, we prove convergence of one-particle density operators in the trace-class topology and estimate the fluctuations as superexponential. This is the first derivation of the so-called nonlinear delta model, widely investigated in the last decades, as a phenomenological model for several physical phenomena.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110866"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110855
T.V. Khanh , A. Raich
The purpose of this paper is to prove that if a pseudoconvex domains satisfies Bell-Ligocka's Condition R and admits a “good” dilation, then the Bergman projection has local -Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that h-extendible domains satisfy our hypotheses.
{"title":"Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type","authors":"T.V. Khanh , A. Raich","doi":"10.1016/j.jfa.2025.110855","DOIUrl":"10.1016/j.jfa.2025.110855","url":null,"abstract":"<div><div>The purpose of this paper is to prove that if a pseudoconvex domains <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> satisfies Bell-Ligocka's Condition R and admits a “good” dilation, then the Bergman projection has local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that <em>h</em>-extendible domains satisfy our hypotheses.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110855"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429911","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 : 2025-02-10DOI: 10.1016/j.jfa.2025.110860
Alexandru Aleman, Frej Dahlin
Given the reproducing kernel k of the Hilbert space we study spaces whose reproducing kernel has the form , where b is a row-contraction on . In terms of reproducing kernels this is the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces [31] in one or several variables. We study some general properties of e.g. when the inclusion map into is compact. Our main result provides a model for reminiscent of the Sz.-Nagy-Foiaş model for contractions (see also [7]). As an application we obtain sufficient conditions for the containment and density of the linear span of in . In the standard cases this reduces to containment and density of polynomials. These methods resolve a very recent conjecture [13] regarding polynomial approximation in spaces with kernel .
{"title":"Generalized de Branges-Rovnyak spaces","authors":"Alexandru Aleman, Frej Dahlin","doi":"10.1016/j.jfa.2025.110860","DOIUrl":"10.1016/j.jfa.2025.110860","url":null,"abstract":"<div><div>Given the reproducing kernel <em>k</em> of the Hilbert space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> we study spaces <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> whose reproducing kernel has the form <span><math><mi>k</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><msup><mrow><mi>b</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span>, where <em>b</em> is a row-contraction on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>. In terms of reproducing kernels this is the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces <span><span>[31]</span></span> in one or several variables. We study some general properties of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> e.g. when the inclusion map into <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is compact. Our main result provides a model for <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> reminiscent of the Sz.-Nagy-Foiaş model for contractions (see also <span><span>[7]</span></span>). As an application we obtain sufficient conditions for the containment and density of the linear span of <span><math><mo>{</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>:</mo><mi>w</mi><mo>∈</mo><mi>X</mi><mo>}</mo></math></span> in <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span>. In the standard cases this reduces to containment and density of polynomials. These methods resolve a very recent conjecture <span><span>[13]</span></span> regarding polynomial approximation in spaces with kernel <span><math><mfrac><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>b</mi><msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup></mrow><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mover><mrow><mi>w</mi></mrow><mo>‾</mo></mover><mo>)</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mo>,</mo><mn>1</mn><mo>≤</mo><mi>m</mi><mo><</mo><mi>β</mi><mo>,</mo><mi>m</mi><mo>∈</mo><mi>N</mi></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110860"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110852
Changying Ding
We show that if is a Bernoulli action of an i.c.c. nonamenable group Γ which is weakly amenable with Cowling-Haagerup constant 1, and is a free ergodic p.m.p. algebraic action of a group Λ, then the isomorphism implies that and are unitarily conjugate. This is obtained by showing a new rigidity result of non properly proximal groups and combining it with a rigidity result of properly proximal groups from [1].
{"title":"A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups","authors":"Changying Ding","doi":"10.1016/j.jfa.2025.110852","DOIUrl":"10.1016/j.jfa.2025.110852","url":null,"abstract":"<div><div>We show that if <span><math><mi>Γ</mi><mspace></mspace><mo>↷</mo><mspace></mspace><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>,</mo><msup><mrow><mi>μ</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo></math></span> is a Bernoulli action of an i.c.c. nonamenable group Γ which is weakly amenable with Cowling-Haagerup constant 1, and <span><math><mi>Λ</mi><mspace></mspace><mo>↷</mo><mspace></mspace><mo>(</mo><mi>Y</mi><mo>,</mo><mi>ν</mi><mo>)</mo></math></span> is a free ergodic p.m.p. algebraic action of a group Λ, then the isomorphism <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo><mo>⋊</mo><mi>Γ</mi><mo>≅</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Y</mi><mo>)</mo><mo>⋊</mo><mi>Λ</mi></math></span> implies that <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> are unitarily conjugate. This is obtained by showing a new rigidity result of non properly proximal groups and combining it with a rigidity result of properly proximal groups from <span><span>[1]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110852"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403637","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 : 2025-02-10DOI: 10.1016/j.jfa.2025.110853
Peng Chen , Danqing He , Xiaochun Li , Lixin Yan
We study the pointwise convergence of the cone multipliers For , and , we prove the pointwise convergence of cone multipliers, i.e. where satisfies . Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.
{"title":"On pointwise convergence of cone multipliers","authors":"Peng Chen , Danqing He , Xiaochun Li , Lixin Yan","doi":"10.1016/j.jfa.2025.110853","DOIUrl":"10.1016/j.jfa.2025.110853","url":null,"abstract":"<div><div>We study the pointwise convergence of the cone multipliers<span><span><span><math><msup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>λ</mi></mrow></msup><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><msubsup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>|</mo><msup><mrow><mi>ξ</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msubsup><mrow><mi>ξ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></mfrac><mo>)</mo></mrow><mrow><mo>+</mo></mrow><mrow><mi>λ</mi></mrow></msubsup><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>ξ</mi><mo>)</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mi>x</mi><mo>⋅</mo><mi>ξ</mi></mrow></msup><mi>d</mi><mi>ξ</mi><mo>.</mo></math></span></span></span> For <span><math><mi>p</mi><mo>≥</mo><mn>2</mn></math></span>, and <span><math><mi>λ</mi><mo>></mo><mi>max</mi><mo></mo><mo>{</mo><mi>n</mi><mo>|</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>}</mo></math></span>, we prove the pointwise convergence of cone multipliers, i.e.<span><span><span><math><munder><mi>lim</mi><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>t</mi></mrow><mrow><mi>λ</mi></mrow></msubsup><mo>(</mo><mi>f</mi><mo>)</mo><mo>→</mo><mi>f</mi><mtext> a.e.</mtext><mo>,</mo></math></span></span></span> where <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> satisfies <span><math><mrow><mtext>supp</mtext><mspace></mspace></mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>⊂</mo><mo>{</mo><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>:</mo><mspace></mspace><mn>1</mn><mo><</mo><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo><mo><</mo><mn>2</mn><mo>}</mo></math></span>. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110853"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419549","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 : 2025-02-10DOI: 10.1016/j.jfa.2025.110863
Huagui Duan , Zihao Qi
In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler . In this paper, we prove this conjecture for a bumpy Finsler if the Morse index of any prime closed geodesic is nonzero.
{"title":"Multiple closed geodesics on Finsler 3-dimensional sphere","authors":"Huagui Duan , Zihao Qi","doi":"10.1016/j.jfa.2025.110863","DOIUrl":"10.1016/j.jfa.2025.110863","url":null,"abstract":"<div><div>In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we prove this conjecture for a bumpy Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> if the Morse index of any prime closed geodesic is nonzero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110863"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421904","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 : 2025-02-07DOI: 10.1016/j.jfa.2025.110862
Mohamed Ali Hamza , Hatem Zaag
We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in some space-time integral, showing a improvement in comparison with previous results obtained in [14], [16].
{"title":"A better bound on blow-up rate for the superconformal semilinear wave equation","authors":"Mohamed Ali Hamza , Hatem Zaag","doi":"10.1016/j.jfa.2025.110862","DOIUrl":"10.1016/j.jfa.2025.110862","url":null,"abstract":"<div><div>We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in some space-time integral, showing a <span><math><mo>|</mo><mi>log</mi><mo></mo><mo>(</mo><mi>T</mi><mo>−</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span> improvement in comparison with previous results obtained in <span><span>[14]</span></span>, <span><span>[16]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110862"},"PeriodicalIF":1.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430122","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 : 2025-01-27DOI: 10.1016/j.jfa.2025.110841
Jonas Blessing , Robert Denk , Michael Kupper , Max Nendel
We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to Γ-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under the semigroup. To overcome this issue, we consider different versions of invariant Lipschitz sets which turn out to be suitable domains for weaker notions of the generator. The so-called Γ-generator is defined as the time derivative with respect to Γ-convergence in the space of upper semicontinuous functions. Under suitable assumptions, we show that the Γ-generator uniquely characterizes the semigroup and is determined by its evaluation at smooth functions. Furthermore, we provide Chernoff approximation results for convex monotone semigroups and show that approximation schemes based on the same infinitesimal behaviour lead to the same semigroup. Our results are applied to semigroups related to stochastic optimal control problems in finite and infinite-dimensional settings as well as Wasserstein perturbations of transition semigroups.
{"title":"Convex monotone semigroups and their generators with respect to Γ-convergence","authors":"Jonas Blessing , Robert Denk , Michael Kupper , Max Nendel","doi":"10.1016/j.jfa.2025.110841","DOIUrl":"10.1016/j.jfa.2025.110841","url":null,"abstract":"<div><div>We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to Γ-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under the semigroup. To overcome this issue, we consider different versions of invariant Lipschitz sets which turn out to be suitable domains for weaker notions of the generator. The so-called Γ-generator is defined as the time derivative with respect to Γ-convergence in the space of upper semicontinuous functions. Under suitable assumptions, we show that the Γ-generator uniquely characterizes the semigroup and is determined by its evaluation at smooth functions. Furthermore, we provide Chernoff approximation results for convex monotone semigroups and show that approximation schemes based on the same infinitesimal behaviour lead to the same semigroup. Our results are applied to semigroups related to stochastic optimal control problems in finite and infinite-dimensional settings as well as Wasserstein perturbations of transition semigroups.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 8","pages":"Article 110841"},"PeriodicalIF":1.7,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：