{"title":"Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem","authors":"Shenyu Liu, Dongyong Yang, Ciqiang Zhuo","doi":"10.1007/s11464-021-0103-x","DOIUrl":null,"url":null,"abstract":"In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p ∈ (1, ∞) is established.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11464-021-0103-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p ∈ (1, ∞) is established.
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