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A generalization of Grünbaum's inequality in RCD(0,N)-spaces RCD(0，N)-空间中gr<s:1> nbaum不等式的推广
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111210
Victor-Emmanuel Brunel , Shin-ichi Ohta , Jordan Serres
{"title":"A generalization of Grünbaum's inequality in RCD(0,N)-spaces","authors":"Victor-Emmanuel Brunel ,&nbsp;Shin-ichi Ohta ,&nbsp;Jordan Serres","doi":"10.1016/j.jfa.2025.111210","DOIUrl":"10.1016/j.jfa.2025.111210","url":null,"abstract":"<div><div>We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to <span><math><mrow><mi>RCD</mi></mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-spaces with <span><math><mi>N</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> as well as weighted Riemannian manifolds of <span><math><msub><mrow><mi>Ric</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≥</mo><mn>0</mn></math></span> for <span><math><mi>N</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span>. Our formulation makes use of the isometric splitting theorem; given a convex set Ω and the Busemann function associated with any straight line, the volume of the intersection of Ω and any sublevel set of the Busemann function that contains a barycenter of Ω is bounded from below in terms of <em>N</em>. We also extend this inequality beyond uniform distributions on convex sets. Moreover, we establish some rigidity results by using the localization method, and the stability problem is also studied.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111210"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155320","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}
引用次数: 0
The Muckenhoupt condition Muckenhoupt条件
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111209
Zoe Nieraeth
{"title":"The Muckenhoupt condition","authors":"Zoe Nieraeth","doi":"10.1016/j.jfa.2025.111209","DOIUrl":"10.1016/j.jfa.2025.111209","url":null,"abstract":"<div><div>The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, pose several conjectures, and prove partial results related to the duality of the Hardy-Littlewood maximal operator. Furthermore, we give an overview of the theory applied to weighted variable Lebesgue, Morrey, and Musielak-Orlicz spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111209"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155323","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}
引用次数: 0
Operators on injective tensor products of separable Banach spaces and spaces with few operators 可分Banach空间和少算子空间的内射张量积上的算子
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111203
Antonio Acuaviva
{"title":"Operators on injective tensor products of separable Banach spaces and spaces with few operators","authors":"Antonio Acuaviva","doi":"10.1016/j.jfa.2025.111203","DOIUrl":"10.1016/j.jfa.2025.111203","url":null,"abstract":"<div><div>We give a characterization of the operators on the injective tensor product <span><math><mi>E</mi><msub><mrow><mover><mrow><mo>⊗</mo></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>ε</mi></mrow></msub><mi>X</mi></math></span> for any separable Banach space <em>E</em> and any (non-separable) Banach space <em>X</em> with few operators, in the sense that any operator <span><math><mi>T</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span> takes the form <span><math><mi>T</mi><mo>=</mo><mi>λ</mi><mi>I</mi><mo>+</mo><mi>S</mi></math></span> for a scalar <span><math><mi>λ</mi><mo>∈</mo><mi>K</mi></math></span> and an operator <em>S</em> with separable range. This is used to give a classification of the complemented subspaces and closed operator ideals of spaces of the form <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ω</mi><mo>×</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> is a locally compact Hausdorff space induced by an almost disjoint family <span><math><mi>A</mi></math></span> such that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>)</mo></math></span> has few operators.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111203"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155317","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}
引用次数: 0
Modulated (C,α)-ergodic theorems in noncommutative Lp-spaces 非交换lp空间中的调制(C,α)-遍历定理
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111208
Guixiang Hong , Yuanyuan Jing , Xin Zhang
{"title":"Modulated (C,α)-ergodic theorems in noncommutative Lp-spaces","authors":"Guixiang Hong ,&nbsp;Yuanyuan Jing ,&nbsp;Xin Zhang","doi":"10.1016/j.jfa.2025.111208","DOIUrl":"10.1016/j.jfa.2025.111208","url":null,"abstract":"<div><div>In this paper, we first establish the weighted <span><math><mo>(</mo><mi>C</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span>-maximal ergodic inequalities for positive Dunford-Schwartz operators acting on noncommutative <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> spaces for <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span>. Utilizing these results, we then present the noncommutative Besicovitch weighted <span><math><mo>(</mo><mi>C</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span>-individual ergodic theorems. Additionally, we also investigate the norm convergence of the Besicovitch weighted <span><math><mo>(</mo><mi>C</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span>-ergodic averages. Some of them appear to be new even in the commutative setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111208"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118843","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}
引用次数: 0
A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator navier - lam<s:1>算子的Mizohata-Takeuchi型先验估计
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111204
J.A. Barceló , A. Ruiz , M.C. Vilela , J. Wright
{"title":"A priori estimates of Mizohata-Takeuchi type for the Navier-Lamé operator","authors":"J.A. Barceló ,&nbsp;A. Ruiz ,&nbsp;M.C. Vilela ,&nbsp;J. Wright","doi":"10.1016/j.jfa.2025.111204","DOIUrl":"10.1016/j.jfa.2025.111204","url":null,"abstract":"<div><div>The Mizohata-Takeuchi conjecture for the resolvent of the Navier-Lamé equation is a weighted estimate with weights in the so-called Mizohata-Takeuchi class for this operator when one approaches the spectrum (Limiting Absorption Principles). We prove this conjecture in dimensions 2 and 3 for weights with a radial majorant in the Mizohata-Takeuchi class. This result can be seen as an extension of the analogue for the Laplacian given in <span><span>[8]</span></span>. We also prove that radial weights in this class are not invariant for the Hardy-Littlewood maximal function, hence the methods in <span><span>[6]</span></span> used to extend estimates for the Laplacian to the Navier-Lamé case, do not work.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111204"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155731","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}
引用次数: 0
Prescribed energy solutions to some scaled problems via a scaled Nehari manifold 用标度Nehari流形求解一些标度问题的规定能量解
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111213
Kanishka Perera , Kaye Silva
{"title":"Prescribed energy solutions to some scaled problems via a scaled Nehari manifold","authors":"Kanishka Perera ,&nbsp;Kaye Silva","doi":"10.1016/j.jfa.2025.111213","DOIUrl":"10.1016/j.jfa.2025.111213","url":null,"abstract":"<div><div>We prove the existence, multiplicity, and bifurcation of solutions with prescribed energy for a broad class of scaled problems by introducing a suitable notion of scaling based Nehari manifold. Applications are given to Schrödinger–Poisson–Slater type equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111213"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155733","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}
引用次数: 0
Maximal inequalities associated to doubling condition for state preserving actions 状态保持动作的倍增条件下的极大不等式
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111201
Panchugopal Bikram , Diptesh Saha
{"title":"Maximal inequalities associated to doubling condition for state preserving actions","authors":"Panchugopal Bikram ,&nbsp;Diptesh Saha","doi":"10.1016/j.jfa.2025.111201","DOIUrl":"10.1016/j.jfa.2025.111201","url":null,"abstract":"<div><div>This article proves maximal inequalities and ergodic theorems for state-preserving actions on von Neumann algebras by amenable, locally compact, second-countable groups equipped with metrics satisfying the doubling condition. The key idea is to use the Hardy–Littlewood maximal inequality, a version of the transference principle and certain norm estimates of differences between ergodic averages and martingales.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 2","pages":"Article 111201"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134801","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}
引用次数: 0
Iterations of the inverse Aluthge transform 逆Aluthge变换的迭代
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111202
Jorge Antezana , Yongdo Lim
{"title":"Iterations of the inverse Aluthge transform","authors":"Jorge Antezana ,&nbsp;Yongdo Lim","doi":"10.1016/j.jfa.2025.111202","DOIUrl":"10.1016/j.jfa.2025.111202","url":null,"abstract":"<div><div>We prove that for <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span> and <span><math><mi>λ</mi><mo>≠</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, the <em>λ</em>-Aluthge transform is a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> diffeomorphism acting on the Lie group of invertible matrices <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. In particular, this provides a one-parameter family in <span><math><msup><mrow><mtext>Diff</mtext></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>. We also characterize the inverse. This characterization is expressed in terms of twisted polar decompositions defined in <em>Bushell's equations and polar decompositions, Mathematische Nachrichten 282 (2009)</em>. This will allow us to study the dynamics of the Aluthge transforms for <span><math><mi>λ</mi><mo>∉</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. In this range of values, we prove that the backward iterations of the Aluthge transform converge. This complements the results in <em>The iterated Aluthge transforms of a matrix converge, Advances in Mathematics, 226 (2011)</em>, where the proof of the forward convergence was proved for <span><math><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. Since neither the backward iterations for <span><math><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> nor the forward iterations for <span><math><mi>λ</mi><mo>∉</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> can converge for a non-normal matrix, this completes the study of the dynamics of the one-parameter family of <em>λ</em>-Aluthge transforms in <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Some open problems and possible future lines of research are mentioned throughout the paper.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 2","pages":"Article 111202"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134800","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}
引用次数: 0
Maximal regularity of solutions for the tempered fractional Cauchy problem 缓变分数阶Cauchy问题解的极大正则性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-17 DOI: 10.1016/j.jfa.2025.111196
Edgardo Alvarez , Carlos Lizama , Marina Murillo-Arcila
{"title":"Maximal regularity of solutions for the tempered fractional Cauchy problem","authors":"Edgardo Alvarez ,&nbsp;Carlos Lizama ,&nbsp;Marina Murillo-Arcila","doi":"10.1016/j.jfa.2025.111196","DOIUrl":"10.1016/j.jfa.2025.111196","url":null,"abstract":"<div><div>Let <em>X</em> be a Banach space. Given a closed linear operator <em>A</em> defined on <em>X</em> we show that, in vector-valued Hölder spaces <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>,</mo><mi>X</mi><mo>)</mo><mspace></mspace><mspace></mspace><mo>(</mo><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></math></span>, maximal regularity for the abstract Cauchy problem can be characterized solely in terms of a spectral property of the operator <em>A</em>, when we equip the Cauchy problem with the tempered fractional derivative. In particular, we show that generators of bounded analytic semigroups admit maximal regularity.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111196"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118842","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}
引用次数: 0
Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838] “量化与求解代数”的勘误[J]。功能。肛门。277 (8)(2019)2815-2838]
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-09-03 DOI: 10.1016/j.jfa.2025.111184
Teun D.H. van Nuland, Lorenzo Pettinari
{"title":"Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838]","authors":"Teun D.H. van Nuland,&nbsp;Lorenzo Pettinari","doi":"10.1016/j.jfa.2025.111184","DOIUrl":"10.1016/j.jfa.2025.111184","url":null,"abstract":"<div><div>In <span><span>[3]</span></span> it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.<span><span><sup>1</sup></span></span> We show here that it does not. Similarly, the Berezin map defined on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></math></span> does not reach all compact operators, contrary to what is claimed in <span><span>[2, II.(2.73)]</span></span>.<span><span><sup>2</sup></span></span> We moreover fill a gap in the proof of injectivity of the Berezin quantization map on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of <span><span>[3]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111184"},"PeriodicalIF":1.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933790","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}
引用次数: 0
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