{"title":"并矢环境中的偏导数、奇异积分与Sobolev空间","authors":"H. Aimar, Juan Comesatti, I. G'omez, Luis Nowak","doi":"10.4208/ata.oa-2021-0051","DOIUrl":null,"url":null,"abstract":"In this note we show that the general theory of vector valued singular integral operators of Calderon-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings\",\"authors\":\"H. Aimar, Juan Comesatti, I. G'omez, Luis Nowak\",\"doi\":\"10.4208/ata.oa-2021-0051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we show that the general theory of vector valued singular integral operators of Calderon-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.\",\"PeriodicalId\":29763,\"journal\":{\"name\":\"Analysis in Theory and Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis in Theory and Applications\",\"FirstCategoryId\":\"95\",\"ListUrlMain\":\"https://doi.org/10.4208/ata.oa-2021-0051\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ata.oa-2021-0051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings
In this note we show that the general theory of vector valued singular integral operators of Calderon-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.
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