与广义calderÓn-zygmund算子相关的换向子的加权紧性准则

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Integral Equations and Applications Pub Date : 2023-06-01 DOI:10.1216/jie.2023.35.235

Li Yang, Qianjun He, Pengtao Li, Kai Zhao

{"title":"与广义calderÓn-zygmund算子相关的换向子的加权紧性准则","authors":"Li Yang, Qianjun He, Pengtao Li, Kai Zhao","doi":"10.1216/jie.2023.35.235","DOIUrl":null,"url":null,"abstract":"Let T be a bounded operator on Lp(ℝn). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb→ on the weighted Lebesgue spaces Lp(ω) with b→∈BMO(ℝn) and ω belonging to the Muckenhoupt weight class Ap∕m′. Further, for b→∈CMO(ℝn), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb→ is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.9000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERÓN–ZYGMUND OPERATORS\",\"authors\":\"Li Yang, Qianjun He, Pengtao Li, Kai Zhao\",\"doi\":\"10.1216/jie.2023.35.235\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let T be a bounded operator on Lp(ℝn). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb→ on the weighted Lebesgue spaces Lp(ω) with b→∈BMO(ℝn) and ω belonging to the Muckenhoupt weight class Ap∕m′. Further, for b→∈CMO(ℝn), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb→ is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.\",\"PeriodicalId\":50176,\"journal\":{\"name\":\"Journal of Integral Equations and Applications\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Integral Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1216/jie.2023.35.235\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Integral Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/jie.2023.35.235","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设T是Lp(n)上的一个有界算子。在T的核满足Hörmander-type估计的假设下，我们得到了多重线性交换子Tb→在加权Lebesgue空间Lp(ω)上的有界性判据，其中b→∈BMO(n)， ω属于Muckenhoupt权类Ap∕m’。进一步，对于消失的平均振荡空间b→∈CMO(n)，建立了Tb→的一个lp加权紧性判据。作为应用，加权的lp有界性和lp紧性准则可应用于𝜃-type Calderón-Zygmund算子及其换向子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERÓN–ZYGMUND OPERATORS

Let T be a bounded operator on Lp(ℝn). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb→ on the weighted Lebesgue spaces Lp(ω) with b→∈BMO(ℝn) and ω belonging to the Muckenhoupt weight class Ap∕m′. Further, for b→∈CMO(ℝn), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb→ is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.