{"title":"Unrestricted Ces\\`aro summability of $d$-dimensional Fourier series and Lebesgue points","authors":"F. Weisz","doi":"10.33205/CMA.859583","DOIUrl":null,"url":null,"abstract":"We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Cesaro means of the Fourier series of the multi-dimensional function $f\\in L_1(\\log L)^{d-1}(\\mathbb{T}^d)\\supset L_p(\\mathbb{T}^d) (1<p<\\infty)$ converge to $f$ at each strong Lebesgue point.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/CMA.859583","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Cesaro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1
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