{"title":"A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary","authors":"Piotr Kot","doi":"10.1007/s11785-024-01532-2","DOIUrl":null,"url":null,"abstract":"<p>We consider a bounded strictly pseudoconvex domain <span>\\(\\Omega \\subset \\mathbb {C}^{n}\\)</span> with <span>\\(C^{2}\\)</span> boundary. Then, we show that any compact Ahlfors–David regular subset of <span>\\(\\partial \\Omega \\)</span> of Hausdorff dimension <span>\\(\\beta \\in (0,2n-1]\\)</span> contains a peak set <i>E</i> of Hausdorff dimension equal to <span>\\(\\beta \\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01532-2","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
We consider a bounded strictly pseudoconvex domain \(\Omega \subset \mathbb {C}^{n}\) with \(C^{2}\) boundary. Then, we show that any compact Ahlfors–David regular subset of \(\partial \Omega \) of Hausdorff dimension \(\beta \in (0,2n-1]\) contains a peak set E of Hausdorff dimension equal to \(\beta \).
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