Pub Date : 2026-03-01Epub Date: 2025-11-11DOI: 10.1016/j.jfa.2025.111272
Ilan Hirshberg , N. Christopher Phillips
We construct an uncountable family of pairwise nonisomorphic simple unital AH algebras with the same Elliott invariant and same radius of comparison. They can be distinguished by a local radius of comparison function, naturally defined on the positive cone of the group.
{"title":"Simple AH algebras with the same Elliott invariant and radius of comparison","authors":"Ilan Hirshberg , N. Christopher Phillips","doi":"10.1016/j.jfa.2025.111272","DOIUrl":"10.1016/j.jfa.2025.111272","url":null,"abstract":"<div><div>We construct an uncountable family of pairwise nonisomorphic simple unital AH algebras with the same Elliott invariant and same radius of comparison. They can be distinguished by a local radius of comparison function, naturally defined on the positive cone of the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> group.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 5","pages":"Article 111272"},"PeriodicalIF":1.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145570819","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 : 2026-02-15Epub Date: 2025-11-10DOI: 10.1016/j.jfa.2025.111274
Dong Han , Jie He , Youde Wang
In this paper we combine Sallof-Coste's Sobolev inequality together with Nash-Moser iteration to study the gradient estimates of non-negative solutions to a class of quasilinear elliptic equation defined on a complete Riemannian manifold with Ricci curvature bounded from below. We obtain the concise gradient estimates of solutions to these equations if , and . As applications, we show that some log-gradient estimates for positive solutions to defined on a complete noncompact manifold , which is closely related to Ricci soliton and p-logarithmic Sobolev inequality.
本文将Sallof-Coste的Sobolev不等式与Nash-Moser迭代相结合，研究了一类拟线性椭圆方程Δpu+ a |∇u|q+Bur+C=0的非负解的梯度估计，该类方程定义在完全黎曼流形（M,g）上，曲率由下有界。我们得到了当A<；0, B≤0，C≤0时这些方程解的简洁梯度估计。作为应用，我们证明了在与Ricci孤子和p-对数Sobolev不等式密切相关的完全非紧流形（M,g）上定义的Δpw−ϵwp−1log （w=0）正解的一些对数梯度估计。
{"title":"Gradient estimates for Δpu + A|∇u|q + Bur + C = 0 on manifolds and applications","authors":"Dong Han , Jie He , Youde Wang","doi":"10.1016/j.jfa.2025.111274","DOIUrl":"10.1016/j.jfa.2025.111274","url":null,"abstract":"<div><div>In this paper we combine Sallof-Coste's Sobolev inequality together with Nash-Moser iteration to study the gradient estimates of non-negative solutions to a class of quasilinear elliptic equation <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>A</mi><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>+</mo><mi>B</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></math></span> defined on a complete Riemannian manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> with Ricci curvature bounded from below. We obtain the concise gradient estimates of solutions to these equations if <span><math><mi>A</mi><mo><</mo><mn>0</mn></math></span>, <span><math><mi>B</mi><mo>≤</mo><mn>0</mn></math></span> and <span><math><mi>C</mi><mo>≤</mo><mn>0</mn></math></span>. As applications, we show that some log-gradient estimates for positive solutions to <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>w</mi><mo>−</mo><mi>ϵ</mi><msup><mrow><mi>w</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>log</mi><mo></mo><mi>w</mi><mo>=</mo><mn>0</mn></math></span> defined on a complete noncompact manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span>, which is closely related to Ricci soliton and <em>p</em>-logarithmic Sobolev inequality.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111274"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145569936","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111253
Jonas Knoerr, Jacopo Ulivelli
A unified framework to investigate polynomial valuations on various spaces of convex functions is introduced. It is shown that these different spaces of valuations can be essentially studied as one single class of valuations defined on a particular cone of convex functions. The corresponding extension problem reduces to a single geometric obstruction on the support of these valuations. As an application, explicit integral representations for a subclass of these valuations are established.
{"title":"Polynomial valuations on convex functions and their maximal extensions","authors":"Jonas Knoerr, Jacopo Ulivelli","doi":"10.1016/j.jfa.2025.111253","DOIUrl":"10.1016/j.jfa.2025.111253","url":null,"abstract":"<div><div>A unified framework to investigate polynomial valuations on various spaces of convex functions is introduced. It is shown that these different spaces of valuations can be essentially studied as one single class of valuations defined on a particular cone of convex functions. The corresponding extension problem reduces to a single geometric obstruction on the support of these valuations. As an application, explicit integral representations for a subclass of these valuations are established.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111253"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465052","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111268
Lea Boßmann , Nikolai Leopold , Sören Petrat , Simone Rademacher
We consider a system of N bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form for . We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.
{"title":"Ground state of Bose gases interacting through singular potentials","authors":"Lea Boßmann , Nikolai Leopold , Sören Petrat , Simone Rademacher","doi":"10.1016/j.jfa.2025.111268","DOIUrl":"10.1016/j.jfa.2025.111268","url":null,"abstract":"<div><div>We consider a system of <em>N</em> bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form <span><math><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn><mi>β</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>v</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>β</mi></mrow></msup><mi>x</mi><mo>)</mo></math></span> for <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111268"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518719","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111254
Cole Durham
In this paper we prove an upper bound for the bottom of the spectrum of the Laplacian on manifolds with Ricci curvature bounded in integral sense. Our arguments rely on the existence of a minimal positive Green's function and its properties.
{"title":"Bottom spectrum estimate under curvature integrability condition","authors":"Cole Durham","doi":"10.1016/j.jfa.2025.111254","DOIUrl":"10.1016/j.jfa.2025.111254","url":null,"abstract":"<div><div>In this paper we prove an upper bound for the bottom of the spectrum of the Laplacian on manifolds with Ricci curvature bounded in integral sense. Our arguments rely on the existence of a minimal positive Green's function and its properties.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111254"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442453","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111266
Zhigang Bao , Jaehun Lee , Xiaocong Xu
In this paper, we consider the rectangular random matrix whose entries are iid with tail for some . We consider the regime as n tends to infinity. Our main interest lies in the right singular vector corresponding to the smallest singular value, which we will refer to as the “bottom singular vector”, denoted by . In this paper, we prove the following phase transition regarding the localization length of : when the localization length is ; when the localization length is of order n. Similar results hold for all right singular vectors around the smallest singular value. The variational definition of the bottom singular vector suggests that the mechanism for this localization-delocalization transition when α goes across 2 is intrinsically different from the one for the top singular vector when α goes across 4.
{"title":"Phase transition for the bottom singular vector of rectangular random matrices","authors":"Zhigang Bao , Jaehun Lee , Xiaocong Xu","doi":"10.1016/j.jfa.2025.111266","DOIUrl":"10.1016/j.jfa.2025.111266","url":null,"abstract":"<div><div>In this paper, we consider the rectangular random matrix <span><math><mi>X</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi><mo>×</mo><mi>n</mi></mrow></msup></math></span> whose entries are iid with tail <span><math><mi>P</mi><mo>(</mo><mo>|</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>|</mo><mo>></mo><mi>t</mi><mo>)</mo><mo>∼</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></math></span> for some <span><math><mi>α</mi><mo>></mo><mn>0</mn></math></span>. We consider the regime <span><math><mi>N</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>/</mo><mi>n</mi><mo>→</mo><mi>a</mi><mo>></mo><mn>1</mn></math></span> as <em>n</em> tends to infinity. Our main interest lies in the right singular vector corresponding to the smallest singular value, which we will refer to as the “bottom singular vector”, denoted by <span><math><mi>u</mi></math></span>. In this paper, we prove the following phase transition regarding the localization length of <span><math><mi>u</mi></math></span>: when <span><math><mi>α</mi><mo><</mo><mn>2</mn></math></span> the localization length is <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>; when <span><math><mi>α</mi><mo>></mo><mn>2</mn></math></span> the localization length is of order <em>n</em>. Similar results hold for all right singular vectors around the smallest singular value. The variational definition of the bottom singular vector suggests that the mechanism for this localization-delocalization transition when <em>α</em> goes across 2 is intrinsically different from the one for the top singular vector when <em>α</em> goes across 4.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111266"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464986","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111250
Eugene Bilokopytov , Enrique García-Sánchez , David de Hevia , Gonzalo Martínez-Cervantes , Pedro Tradacete
A well-known theorem due to R. C. James states that a Banach space is reflexive if and only if every bounded linear functional attains its norm. In this note we study Banach lattices on which every (real-valued) lattice homomorphism attains its norm. Contrary to what happens in the Banach space setting, we show that this property is not invariant under lattice isomorphisms. Namely, we show that in an AM-space every lattice homomorphism attains its norm, whereas every infinite-dimensional space admits an equivalent lattice norm with a lattice homomorphism which does not attain its norm. Furthermore, we characterize coordinate functionals of atoms and show that whenever a Banach lattice X supports a strictly positive functional, there exists a renorming with the property that the only (non-trivial) lattice homomorphisms attaining their norm are precisely these coordinate functionals. As a consequence, one can exhibit examples of Dedekind complete Banach lattices admitting a renorming with a non-norm-attaining lattice homomorphism, answering negatively questions posed by Dantas, Rodríguez Abellán, Rueda Zoca and the fourth author.
{"title":"Norm-attaining lattice homomorphisms and renormings of Banach lattices","authors":"Eugene Bilokopytov , Enrique García-Sánchez , David de Hevia , Gonzalo Martínez-Cervantes , Pedro Tradacete","doi":"10.1016/j.jfa.2025.111250","DOIUrl":"10.1016/j.jfa.2025.111250","url":null,"abstract":"<div><div>A well-known theorem due to R. C. James states that a Banach space is reflexive if and only if every bounded linear functional attains its norm. In this note we study Banach lattices on which every (real-valued) lattice homomorphism attains its norm. Contrary to what happens in the Banach space setting, we show that this property is not invariant under lattice isomorphisms. Namely, we show that in an AM-space every lattice homomorphism attains its norm, whereas every infinite-dimensional <span><math><mi>C</mi><mo>(</mo><mi>K</mi><mo>)</mo></math></span> space admits an equivalent lattice norm with a lattice homomorphism which does not attain its norm. Furthermore, we characterize coordinate functionals of atoms and show that whenever a Banach lattice <em>X</em> supports a strictly positive functional, there exists a renorming with the property that the only (non-trivial) lattice homomorphisms attaining their norm are precisely these coordinate functionals. As a consequence, one can exhibit examples of Dedekind complete Banach lattices admitting a renorming with a non-norm-attaining lattice homomorphism, answering negatively questions posed by Dantas, Rodríguez Abellán, Rueda Zoca and the fourth author.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111250"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464988","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111263
Jin Bong Lee , Jinsol Seo
In this paper, we investigate bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees bounds of the maximal operators for each p. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay.
{"title":"Maximal operators given by Fourier multipliers with dilation of fractional dimensions","authors":"Jin Bong Lee , Jinsol Seo","doi":"10.1016/j.jfa.2025.111263","DOIUrl":"10.1016/j.jfa.2025.111263","url":null,"abstract":"<div><div>In this paper, we investigate <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> bounds of the maximal operators for each <em>p</em>. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111263"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465053","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111259
Weichao Guo , Shifei Lin , Guoping Zhao
<div><div>The first purpose of this paper is to consider the optimal estimate for the operator norm <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>L</mi><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msub></math></span> of time-frequency localization operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> with normalized Gaussian window <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and symbol function <em>F</em>, under the assumptions that <span><math><mi>F</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> with <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>F</mi><mo>|</mo><mo>=</mo><mo>|</mo><mo>{</mo><mi>z</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>d</mi></mrow></msup><mo>:</mo><mo>|</mo><mi>F</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>|</mo><mo>≠</mo><mn>0</mn><mo>}</mo><mo>|</mo><mo>≤</mo><mi>M</mi></math></span>. To achieve this goal, we use the connection between such an optimal estimate and the restricted Hölder's inequality associated with a Gaussian weight. Based on this connection, our second purpose is to study a general version of restricted-type Hölder inequalities, which is of independent interest. We provide optimal upper bounds for the quantity <span><math><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub><mo>|</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>d</mi><mi>x</mi></math></span> with general functions <em>g</em>, assuming <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> with <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>f</mi><mo>|</mo><mo>≤</mo><mi>M</mi></math></span>. We also give a full characterization of the optimal functions, whose shape depends on <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>f</mi><mo>|</mo></math></span>, <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>g</mi><mo>|</mo></math></span> and the magnitude relationship between <span><math><msup><mrow><mo>(</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></msub><mo>/</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>)</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><msu
{"title":"A sharp restricted Hölder's inequality and its application to the norm of localization operators","authors":"Weichao Guo , Shifei Lin , Guoping Zhao","doi":"10.1016/j.jfa.2025.111259","DOIUrl":"10.1016/j.jfa.2025.111259","url":null,"abstract":"<div><div>The first purpose of this paper is to consider the optimal estimate for the operator norm <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>L</mi><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msub></math></span> of time-frequency localization operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> with normalized Gaussian window <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and symbol function <em>F</em>, under the assumptions that <span><math><mi>F</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> with <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>F</mi><mo>|</mo><mo>=</mo><mo>|</mo><mo>{</mo><mi>z</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>d</mi></mrow></msup><mo>:</mo><mo>|</mo><mi>F</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>|</mo><mo>≠</mo><mn>0</mn><mo>}</mo><mo>|</mo><mo>≤</mo><mi>M</mi></math></span>. To achieve this goal, we use the connection between such an optimal estimate and the restricted Hölder's inequality associated with a Gaussian weight. Based on this connection, our second purpose is to study a general version of restricted-type Hölder inequalities, which is of independent interest. We provide optimal upper bounds for the quantity <span><math><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub><mo>|</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>d</mi><mi>x</mi></math></span> with general functions <em>g</em>, assuming <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> with <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>f</mi><mo>|</mo><mo>≤</mo><mi>M</mi></math></span>. We also give a full characterization of the optimal functions, whose shape depends on <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>f</mi><mo>|</mo></math></span>, <span><math><mo>|</mo><mover><mrow><mtext>supp</mtext></mrow><mrow><mo>˜</mo></mrow></mover><mspace></mspace><mi>g</mi><mo>|</mo></math></span> and the magnitude relationship between <span><math><msup><mrow><mo>(</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></msub><mo>/</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>)</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><msu","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111259"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464992","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111248
Juncheng Wei , Qidi Zhang , Yifu Zhou
<div><div>We construct global growing, bounded, and decaying solutions to the 1-equivariant harmonic map flow from <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> into <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi><mi>r</mi></mrow></msub><mo>+</mo><mfrac><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow><mrow><mi>r</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>sin</mi><mo></mo><mo>(</mo><mn>2</mn><mi>v</mi><mo>)</mo></mrow><mrow><mn>2</mn><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo></mtd><mtd><mspace></mspace></mtd><mtd><mo>(</mo><mi>r</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>×</mo><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>∞</mo><mo>)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>v</mi><mo>(</mo><mi>r</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>,</mo></mtd><mtd><mspace></mspace></mtd><mtd><mi>r</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></mtd></mtr></mtable></mrow></math></span></span></span> for <span><math><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> sufficiently large and the initial data <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo></math></span> satisfying<span><span><span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mi>π</mi><mspace></mspace><mtext> and </mtext><mspace></mspace><mrow><mo>|</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>|</mo></mrow><mo>≲</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>max</mi><mo></mo><mo>{</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>1</mn><mo>}</mo></mrow></msubsup><msup><mrow><mi>r</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup><mspace></mspace><mtext> as </mtext><mspace></mspace><mi>r</mi><mo>→</mo><mo>∞</mo><mo>,</mo><mspace></mspace><mi>γ</mi><mo>></mo><mn>1</mn><mo>.</mo></math></span></span></span> These global solutions exhibit the following trichotomy long-time asymptotic behavior<span><span><span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>t</mi><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo></mrow></msub><mo>∼</mo><mrow><mo>{</mo><mtable>
我们构造了从R2到S2{vt=vrr+vrr−sin (2v)2r2的1-等变调和映射流的整体增长、有界和衰减解，(r,t)∈r+ x (t0,∞)v(r,t0)=v0(r),r∈r+，对于t0足够大且初始数据v0(r)满足v0(0)=π和|v0(r)|≥t0max (0，γ2−1}r1−γ为r→∞，γ>1。这些全局解表现出如下的三分法长期渐近行为‖vr（⋅,t）‖L∞([0,∞))~ {tγ2−1ln (t), if 1<γ<21, if γ=2ln (t), if γ>2。
{"title":"Trichotomy dynamics of the 1-equivariant harmonic map flow","authors":"Juncheng Wei , Qidi Zhang , Yifu Zhou","doi":"10.1016/j.jfa.2025.111248","DOIUrl":"10.1016/j.jfa.2025.111248","url":null,"abstract":"<div><div>We construct global growing, bounded, and decaying solutions to the 1-equivariant harmonic map flow from <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> into <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi><mi>r</mi></mrow></msub><mo>+</mo><mfrac><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow><mrow><mi>r</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>sin</mi><mo></mo><mo>(</mo><mn>2</mn><mi>v</mi><mo>)</mo></mrow><mrow><mn>2</mn><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo></mtd><mtd><mspace></mspace></mtd><mtd><mo>(</mo><mi>r</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>×</mo><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>∞</mo><mo>)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>v</mi><mo>(</mo><mi>r</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>,</mo></mtd><mtd><mspace></mspace></mtd><mtd><mi>r</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></mtd></mtr></mtable></mrow></math></span></span></span> for <span><math><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> sufficiently large and the initial data <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo></math></span> satisfying<span><span><span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mi>π</mi><mspace></mspace><mtext> and </mtext><mspace></mspace><mrow><mo>|</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>|</mo></mrow><mo>≲</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>max</mi><mo></mo><mo>{</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>1</mn><mo>}</mo></mrow></msubsup><msup><mrow><mi>r</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup><mspace></mspace><mtext> as </mtext><mspace></mspace><mi>r</mi><mo>→</mo><mo>∞</mo><mo>,</mo><mspace></mspace><mi>γ</mi><mo>></mo><mn>1</mn><mo>.</mo></math></span></span></span> These global solutions exhibit the following trichotomy long-time asymptotic behavior<span><span><span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>t</mi><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo></mrow></msub><mo>∼</mo><mrow><mo>{</mo><mtable>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111248"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518721","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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