Journal of Functional Analysis最新文献

Ryll-Wojtaszczyk formulas for bihomogeneous polynomials on the sphere 球上双齐次多项式的ryl - wojtaszczyk公式

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111360

A. Defant , D. Galicer , M. Mansilla , M. Mastyło , S. Muro

引用次数: 0

The convergence and uniqueness of a discrete-time nonlinear Markov chain 离散非线性马尔可夫链的收敛性和唯一性

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111367

Ruowei Li , Florentin Münch

{"title":"The convergence and uniqueness of a discrete-time nonlinear Markov chain","authors":"Ruowei Li , Florentin Münch","doi":"10.1016/j.jfa.2026.111367","DOIUrl":"10.1016/j.jfa.2026.111367","url":null,"abstract":"<div><div>In this paper, we prove the convergence and uniqueness of a general discrete-time nonlinear Markov chain with specific conditions. The results have important applications in discrete differential geometry. First, we prove the discrete-time Ollivier Ricci curvature flow <math><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>≔</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><msub><mrow><mi>κ</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mo>)</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></math> converges to a constant curvature metric on a finite weighted graph. As shown in [30, Theorem 5.1], a Laplacian separation principle holds on a locally finite graph with nonnegative Ollivier curvature. We further prove that the Laplacian separation flow converges to the constant Laplacian solution and generalizes the result to nonlinear p-Laplace operators. Moreover, our results can also be applied to study the long-time behavior in the nonlinear Dirichlet forms theory and nonlinear Perron-Frobenius theory. Finally, we define the Ollivier Ricci curvature of the nonlinear Markov chain which is consistent with the classical Ollivier Ricci curvature, sectional curvature [5], coarse Ricci curvature on hypergraphs [14] and the modified Ollivier Ricci curvature for p-Laplace. We also establish the convergence results for the nonlinear Markov chain with nonnegative Ollivier Ricci curvature.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111367"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076935","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 simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball 球面上的索博列夫反不等式和单位球上的索博列夫迹不等式的简单证明

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-26 DOI: 10.1016/j.jfa.2026.111380

Runmin Gong , Qiaohua Yang , Shihong Zhang

{"title":"A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball","authors":"Runmin Gong , Qiaohua Yang , Shihong Zhang","doi":"10.1016/j.jfa.2026.111380","DOIUrl":"10.1016/j.jfa.2026.111380","url":null,"abstract":"<div><div>Frank et al. (2022) [38] stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we demonstrate that reverse Sobolev inequalities of order <math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>1</mn><mo>)</mo></math> on the n-sphere can be readily derived from the reversed HLS inequalities. For the case <math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>1</mn><mo>,</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>)</mo></math>, we present a simple proof of reverse Sobolev inequalities by using the center of mass condition introduced by Hang. In addition, applying this approach, we establish the quantitative stability of reverse Sobolev inequalities of order <math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>1</mn><mo>,</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>)</mo></math> with explicit lower bounds. Finally, by using conformally covariant boundary operators and reverse Sobolev inequalities, we derive Sobolev trace inequalities on the unit ball.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111380"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076937","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

Transition threshold of Couette flow for 2D Boussinesq equations 二维Boussinesq方程的Couette流的过渡阈值

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111383

Xiaoxia Ren , Dongyi Wei

引用次数: 0

On a class of nonlinear BGK-type kinetic equations with density dependent collision rates 一类具有密度相关碰撞率的非线性bgk型动力学方程

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111376

Josephine Evans , Daniel Morris , Havva Yoldaş

引用次数: 0

Sharp ℓp inequalities for discrete singular integrals on the lattice Zd 晶格Zd上离散奇异积分的尖锐不等式

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111359

Rodrigo Bañuelos , Daesung Kim , Mateusz Kwaśnicki

{"title":"Sharp ℓp inequalities for discrete singular integrals on the lattice Zd","authors":"Rodrigo Bañuelos , Daesung Kim , Mateusz Kwaśnicki","doi":"10.1016/j.jfa.2026.111359","DOIUrl":"10.1016/j.jfa.2026.111359","url":null,"abstract":"<div><div>This paper investigates higher dimensional versions of the longstanding conjecture verified in [11] that the <math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-norm of the discrete Hilbert transform on the integers is the same as the <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-norm of the Hilbert transform on the real line. It computes the <math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-norms of a family of discrete operators on the lattice <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math>, <math><mi>d</mi><mo>≥</mo><mn>1</mn></math>. They are discretizations of a new class of singular integrals on <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math> that have the same kernels as the classical Riesz transforms near zero and similar behavior at infinity. The discrete operators have the same p-norms as the classical Riesz transforms on <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math>. They are constructed as conditional expectations of martingale transforms of Doob h-processes conditioned to exit the upper-half space <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math> only on the lattice <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math>. The paper also presents a discrete analogue of the classical method of rotations which gives the norm of a different variant of discrete Riesz transforms on <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math>. Along the way a new proof is given based on Fourier transform techniques of the key identity used to identify the norm of the discrete Hilbert transform in [11]. Open problems are stated.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111359"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057598","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

Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison 用能量比较法估计三流形中常平均曲率曲面的指数

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111375

Luca Seemungal, Ben Sharp

引用次数: 0

Large deviation principles for stochastic nonlinear Schrödinger equations driven by Lévy noise l<s:1>杂讯驱动随机非线性Schrödinger方程的大偏差原理

IF 1.6 2区数学

Journal of Functional Analysis Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111377

Jiahui Zhu , Wei Liu , Jianliang Zhai

引用次数: 0

Thin spectra for periodic and ergodic word models 周期和遍历词模型的薄谱