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Some product problem of Toeplitz and Hankel operators on the bidisk 双盘上Toeplitz算子和Hankel算子的乘积问题
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-06 DOI: 10.1016/j.jmaa.2025.129646
Yong Chen , Ya Liu , Jiayun Shen , Qi Wu
{"title":"Some product problem of Toeplitz and Hankel operators on the bidisk","authors":"Yong Chen ,&nbsp;Ya Liu ,&nbsp;Jiayun Shen ,&nbsp;Qi Wu","doi":"10.1016/j.jmaa.2025.129646","DOIUrl":"10.1016/j.jmaa.2025.129646","url":null,"abstract":"<div><div>The paper focuses on some product problem of Toeplitz operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ψ</mi></mrow></msub></math></span> with pluriharmonic symbol <em>ψ</em> and Hankel operator <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> with general <em>φ</em> on the Hardy space of the bidisk. It completely solves when <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ψ</mi></mrow></msub></math></span> commutes with <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span>. Also, the product of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ψ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> being another Toeplitz operator or Hankel operator is characterized.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129646"},"PeriodicalIF":1.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fredholm weighted composition operators on analytic Lipschitz algebras 解析Lipschitz代数上的Fredholm加权复合算子
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-06 DOI: 10.1016/j.jmaa.2025.129643
Shadi Behrouzi, Hakimeh Mahyar
{"title":"Fredholm weighted composition operators on analytic Lipschitz algebras","authors":"Shadi Behrouzi,&nbsp;Hakimeh Mahyar","doi":"10.1016/j.jmaa.2025.129643","DOIUrl":"10.1016/j.jmaa.2025.129643","url":null,"abstract":"<div><div>In this paper, we will first show that any weighted composition operator on analytic Lipschitz algebras and on analytic little Lipschitz algebras is injective provided the underlying compact set has dense interior, and we characterize completely the surjectivity of them. Then we will give necessary conditions, and in a special case, a sufficient condition for a weighted composition operator on these algebras to be Fredholm. Finally, we note that all the results obtained about analytic (little) Lipschitz algebras are also valid for the uniform algebra <span><math><mi>A</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> where <em>X</em> is a compact subset of the complex plane <span><math><mi>C</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129643"},"PeriodicalIF":1.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Asymptotic analysis and the Weierstrass theorem in dual spaces 对偶空间中的渐近分析与Weierstrass定理
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-06 DOI: 10.1016/j.jmaa.2025.129635
Fatemeh Fakhar , Majid Fakhar , Hamid Reza Hajisharifi
{"title":"Asymptotic analysis and the Weierstrass theorem in dual spaces","authors":"Fatemeh Fakhar ,&nbsp;Majid Fakhar ,&nbsp;Hamid Reza Hajisharifi","doi":"10.1016/j.jmaa.2025.129635","DOIUrl":"10.1016/j.jmaa.2025.129635","url":null,"abstract":"<div><div>In this paper, we introduce a new concept of asymptotic function to derive the Weierstrass theorem for transfer weakly lower continuous functions without coercivity condition in dual spaces that are endowed with the weak<sup>⁎</sup> topology. Moreover, by this asymptotic function we establish a necessary and sufficient condition for a minimization problem within the framework of transfer weakly lower continuous and quasiconvex functions in dual spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129635"},"PeriodicalIF":1.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Global well-posedness for the 3D incompressible MHD system with a class of large initial data 具有一类大初始数据的三维不可压缩MHD系统的全局适定性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-06 DOI: 10.1016/j.jmaa.2025.129645
Zhibin Wang
{"title":"Global well-posedness for the 3D incompressible MHD system with a class of large initial data","authors":"Zhibin Wang","doi":"10.1016/j.jmaa.2025.129645","DOIUrl":"10.1016/j.jmaa.2025.129645","url":null,"abstract":"<div><div>We study the global well-posedness for the 3D Magnetohydrodynamics (MHD) system with a class of large initial data. This type of data varies slowly in the vertical direction and its norm blows up in the largest critical space <span><math><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mo>∞</mo><mo>,</mo><mo>∞</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></math></span> at a rate of <span><math><msup><mrow><mi>ε</mi></mrow><mrow><mi>δ</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> for <span><math><mn>0</mn><mo>≤</mo><mi>δ</mi><mo>&lt;</mo><mn>1</mn></math></span> as <em>ε</em> tends to zero. With this type of data, we prove the system generates global solutions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> when <span><math><mn>0</mn><mo>&lt;</mo><mi>δ</mi><mo>&lt;</mo><mn>1</mn></math></span>. When <span><math><mi>δ</mi><mo>=</mo><mn>0</mn></math></span>, we prove the system is globally well-posed in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129645"},"PeriodicalIF":1.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 role of the toxin effect in the predator-prey system with prey-taxis 毒素效应在具有趋向性的捕食者-猎物系统中的作用
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-06 DOI: 10.1016/j.jmaa.2025.129639
Guiling Wu , Jingyu Li , Lu Xu
{"title":"The role of the toxin effect in the predator-prey system with prey-taxis","authors":"Guiling Wu ,&nbsp;Jingyu Li ,&nbsp;Lu Xu","doi":"10.1016/j.jmaa.2025.129639","DOIUrl":"10.1016/j.jmaa.2025.129639","url":null,"abstract":"<div><div>This paper concerns the population dynamics of a predator-prey model with the effect of prey toxicity, which describes the phenomena that the preys release their own toxins to predators as a defensive measure for survival. Compared with the classical predator-prey system, this system has stronger nonlinear coupling structure due to the inclusion of a prey toxicity. By delicate decoupling energy estimates, we prove that this system possesses a globally bounded classical solution in a smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>(</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></math></span> with homogeneous Neumann boundary conditions. Furthermore, we find a threshold to classify the global asymptotic stability of the prey-only steady state and the coexistence steady state by constructing suitable Lyapunov functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129639"},"PeriodicalIF":1.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Decay estimates for nonlinear Schrödinger equation with the inverse-square potential 具有平方反比势的非线性Schrödinger方程的衰减估计
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI: 10.1016/j.jmaa.2025.129631
Jialu Wang , Chengbin Xu , Fang Zhang
{"title":"Decay estimates for nonlinear Schrödinger equation with the inverse-square potential","authors":"Jialu Wang ,&nbsp;Chengbin Xu ,&nbsp;Fang Zhang","doi":"10.1016/j.jmaa.2025.129631","DOIUrl":"10.1016/j.jmaa.2025.129631","url":null,"abstract":"<div><div>In this paper, we study the dispersive decay estimates for solution to the <span><math><mn>3</mn><mi>D</mi></math></span> energy-critical nonlinear Schrödinger equation with an inverse-square operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span> where the operator is denoted by <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span> with the constant <span><math><mi>a</mi><mo>≥</mo><mn>0</mn></math></span>. Inspired by the work of <span><span>[20]</span></span>, <span><span>[23]</span></span>, we first establish that the solutions exhibit <span><math><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> uniform regularity, derive the Lorentz-Strichartz estimates, and then obtain the desired decay estimates using the bootstrap argument. The key ingredients of our approach include the equivalence of Sobolev norms and the fractional product rule.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129631"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Inversion formula, unique continuation property, and range characterization of the mixed ray transform in R2 R2中混合射线变换的反演公式、独特的延拓性质和范围表征
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI: 10.1016/j.jmaa.2025.129637
Rohit Kumar Mishra , Suman Kumar Sahoo , Chandni Thakkar
{"title":"Inversion formula, unique continuation property, and range characterization of the mixed ray transform in R2","authors":"Rohit Kumar Mishra ,&nbsp;Suman Kumar Sahoo ,&nbsp;Chandni Thakkar","doi":"10.1016/j.jmaa.2025.129637","DOIUrl":"10.1016/j.jmaa.2025.129637","url":null,"abstract":"<div><div>In this article, we study various aspects of the mixed ray transform of <span><math><mo>(</mo><mi>k</mi><mo>+</mo><mi>ℓ</mi><mo>)</mo></math></span>-tensor fields that are symmetric in its first <em>k</em> and last <em>ℓ</em> indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129637"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143924918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Null controllability for stochastic heat equations with singular inverse-square potentials 具有奇异平方反比势的随机热方程的零可控性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI: 10.1016/j.jmaa.2025.129633
Luchuan Zhou, Bo You
{"title":"Null controllability for stochastic heat equations with singular inverse-square potentials","authors":"Luchuan Zhou,&nbsp;Bo You","doi":"10.1016/j.jmaa.2025.129633","DOIUrl":"10.1016/j.jmaa.2025.129633","url":null,"abstract":"<div><div>This paper is devoted to the analysis of control properties for stochastic heat equations with a singular inverse-square potential arising in quantum mechanics and combustion theory. Using some results in functional analysis, we demonstrate that the null controllability of this system can be reduced to the observability of a backward stochastic system introduced here. Then, we prove the desired observability inequality by establishing a new Carleman inequality for the backward system. Our proof of Carleman inequality is based on Itô's formula, a splitting argument on the domain, two improved versions of the Hardy inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129633"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Disjointly strictly singular and L-weakly compact inclusions between variable Lebesgue spaces 可变Lebesgue空间间的严格奇异和l -弱紧包含
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI: 10.1016/j.jmaa.2025.129634
Francisco L. Hernández , César Ruiz , Mauro Sanchiz
{"title":"Disjointly strictly singular and L-weakly compact inclusions between variable Lebesgue spaces","authors":"Francisco L. Hernández ,&nbsp;César Ruiz ,&nbsp;Mauro Sanchiz","doi":"10.1016/j.jmaa.2025.129634","DOIUrl":"10.1016/j.jmaa.2025.129634","url":null,"abstract":"<div><div>Disjointly strictly singular inclusions between variable Lebesgue spaces <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of <em>L</em>-weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo><mo>↪</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> is not disjointly strictly singular. No restrictions on the exponent are imposed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129634"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Averaging principle for a class of distribution dependent slow-fast stochastic differential equations driven by fractional Brownian motion and standard Brownian motion 分数布朗运动和标准布朗运动驱动的一类与分布相关的慢速随机微分方程的平均原理
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI: 10.1016/j.jmaa.2025.129628
Shitao Liu
{"title":"Averaging principle for a class of distribution dependent slow-fast stochastic differential equations driven by fractional Brownian motion and standard Brownian motion","authors":"Shitao Liu","doi":"10.1016/j.jmaa.2025.129628","DOIUrl":"10.1016/j.jmaa.2025.129628","url":null,"abstract":"<div><div>This paper investigates a class of distribution dependent slow-fast stochastic differential equations driven simultaneously by multidimensional standard Brownian motions and a multidimensional fractional Brownian motion with Hurst parameter <span><math><mn>1</mn><mo>/</mo><mn>2</mn><mo>&lt;</mo><mi>H</mi><mo>&lt;</mo><mn>1</mn></math></span>. Existence and uniqueness of the system is proved by using the Picard iteration. Moreover, strong averaging principle is studied to show that slow variable of the system can be efficiently approximated by solution of associated averaged stochastic differential equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129628"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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