微分形式的分数积分和奇异积分对易子的不等式

IF 1.1 3区数学 Q1 MATHEMATICS Journal of Mathematical Inequalities Pub Date : 2023-01-01 DOI:10.7153/jmi-2023-17-28

Jinl ng Niu, Guan an Shi, S. Ding, Yuming Xing

{"title":"微分形式的分数积分和奇异积分对易子的不等式","authors":"Jinl ng Niu, Guan an Shi, S. Ding, Yuming Xing","doi":"10.7153/jmi-2023-17-28","DOIUrl":null,"url":null,"abstract":". In this paper, we de ﬁ ne the commutators of fractional integral operators and Calder´on-Zygmund singular integral operators on differential forms, and give the suf ﬁ cient and necessary conditions for these commutators to be bounded on weighted Lebesgue spaces. As an application, the Caccioppoli-type inequalities with Orlicz norm for commutators of Calder´on-Zygmund singular integral operators on differential forms are obtained.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inequalities for commutators of fractional integrals and singular integrals on differential forms\",\"authors\":\"Jinl ng Niu, Guan an Shi, S. Ding, Yuming Xing\",\"doi\":\"10.7153/jmi-2023-17-28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we de ﬁ ne the commutators of fractional integral operators and Calder´on-Zygmund singular integral operators on differential forms, and give the suf ﬁ cient and necessary conditions for these commutators to be bounded on weighted Lebesgue spaces. As an application, the Caccioppoli-type inequalities with Orlicz norm for commutators of Calder´on-Zygmund singular integral operators on differential forms are obtained.\",\"PeriodicalId\":49165,\"journal\":{\"name\":\"Journal of Mathematical Inequalities\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Inequalities\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7153/jmi-2023-17-28\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Inequalities","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/jmi-2023-17-28","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

．本文定义了分数阶积分算子和Calder´on- zygmund奇异积分算子在微分形式上的对易子，并给出了这些对易子在加权Lebesgue空间上有界的充分必要条件。作为应用，得到了微分形式Calder´on- zygmund奇异积分算子对易子的具有Orlicz范数的caccioppolii型不等式。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Inequalities for commutators of fractional integrals and singular integrals on differential forms

. In this paper, we de ﬁ ne the commutators of fractional integral operators and Calder´on-Zygmund singular integral operators on differential forms, and give the suf ﬁ cient and necessary conditions for these commutators to be bounded on weighted Lebesgue spaces. As an application, the Caccioppoli-type inequalities with Orlicz norm for commutators of Calder´on-Zygmund singular integral operators on differential forms are obtained.

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 Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.