{"title":"Homogeneous Besov Space in Dunkl setting","authors":"Mengmeng Dou, Jiashu Zhang","doi":"arxiv-2408.00340","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to characterize the homogeneous Besov space in\nthe Dunkl setting. We utilize a new discrete reproducing formula, that is, the\nbuilding blocks are differences of the Dunkl-Poisson kernel which involves both\nthe Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the\nDunkl setting, new test functions and distributions are introduced, and a new\ndecomposition is established.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"75 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.00340","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The purpose of this paper is to characterize the homogeneous Besov space in
the Dunkl setting. We utilize a new discrete reproducing formula, that is, the
building blocks are differences of the Dunkl-Poisson kernel which involves both
the Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the
Dunkl setting, new test functions and distributions are introduced, and a new
decomposition is established.
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