{"title":"论弱外厚域特征函数的规律性","authors":"Winfried Sickel","doi":"10.1134/s0081543823050085","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>\\(E\\)</span> be a domain in <span>\\(\\mathbb R^d\\)</span>. We investigate the regularity of the characteristic function <span>\\(\\mathcal X_E\\)</span> depending on the behavior of the <span>\\(\\delta\\)</span>-neighborhoods of the boundary of <span>\\(E\\)</span>. The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains\",\"authors\":\"Winfried Sickel\",\"doi\":\"10.1134/s0081543823050085\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> Let <span>\\\\(E\\\\)</span> be a domain in <span>\\\\(\\\\mathbb R^d\\\\)</span>. We investigate the regularity of the characteristic function <span>\\\\(\\\\mathcal X_E\\\\)</span> depending on the behavior of the <span>\\\\(\\\\delta\\\\)</span>-neighborhoods of the boundary of <span>\\\\(E\\\\)</span>. The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces. </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0081543823050085\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823050085","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
Abstract Let \(E\) be a domain in \(\mathbb R^d\).我们研究了特征函数 \(\mathcal X_E\) 的正则性，它取决于 \(E\) 边界的 \(\delta\)-neighborhoods 的行为。正则性是通过尼克尔斯基-贝索夫空间和利佐金-特里贝尔空间来衡量的。
On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains
Abstract
Let \(E\) be a domain in \(\mathbb R^d\). We investigate the regularity of the characteristic function \(\mathcal X_E\) depending on the behavior of the \(\delta\)-neighborhoods of the boundary of \(E\). The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces.
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