同质类型空间上与可接受函数相关的分数积分的加权有界性

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-10 DOI:10.1007/s13540-024-00300-5

Gaigai Qin, Xing Fu

{"title":"同质类型空间上与可接受函数相关的分数积分的加权有界性","authors":"Gaigai Qin, Xing Fu","doi":"10.1007/s13540-024-00300-5","DOIUrl":null,"url":null,"abstract":"Let \\(({{\\mathcal {X}}},d,\\mu )\\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \\(I_\\beta \\) associated with admissible functions and its commutators. Similarly to \\(I_\\beta \\), corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type\",\"authors\":\"Gaigai Qin, Xing Fu\",\"doi\":\"10.1007/s13540-024-00300-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\(({{\\\\mathcal {X}}},d,\\\\mu )\\\\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \\\\(I_\\\\beta \\\\) associated with admissible functions and its commutators. Similarly to \\\\(I_\\\\beta \\\\), corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.\",\"PeriodicalId\":48928,\"journal\":{\"name\":\"Fractional Calculus and Applied Analysis\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Calculus and Applied Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00300-5\",\"RegionNum\":2,\"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":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00300-5","RegionNum":2,"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

设 \(({{\mathcal {X}}},d,\mu )\) 是 Coifman 和 Weiss 意义上的均质型空间。在本文中，我们首先为各种最大函数建立了几个加权规范估计。然后，我们证明了与可容许函数及其换元相关的分数积分 \(I_\beta \) 的加权有界性。与 \(I_\beta \) 类似，本文也包含了与可允许函数相关的卡尔德龙-齐格蒙特算子 T 的相应结果。

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

Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type

Let \(({{\mathcal {X}}},d,\mu )\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \(I_\beta \) associated with admissible functions and its commutators. Similarly to \(I_\beta \), corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.