{"title":"Hardy空间的扩展域","authors":"Shahaboddin Shaabani","doi":"10.4064/sm220726-30-5","DOIUrl":null,"url":null,"abstract":"We show that a proper open subset $\\Omega \\subset \\mathbb R^{n}$ is an extension domain for $H^p$ ($0 \\lt p\\le 1$) if and only if it satisfies a certain geometric condition. When $n(1/p-1)\\in \\mathbb N$, this condition is equivalent to the global Markov c","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extension domains for Hardy spaces\",\"authors\":\"Shahaboddin Shaabani\",\"doi\":\"10.4064/sm220726-30-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that a proper open subset $\\\\Omega \\\\subset \\\\mathbb R^{n}$ is an extension domain for $H^p$ ($0 \\\\lt p\\\\le 1$) if and only if it satisfies a certain geometric condition. When $n(1/p-1)\\\\in \\\\mathbb N$, this condition is equivalent to the global Markov c\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/sm220726-30-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/sm220726-30-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We show that a proper open subset $\Omega \subset \mathbb R^{n}$ is an extension domain for $H^p$ ($0 \lt p\le 1$) if and only if it satisfies a certain geometric condition. When $n(1/p-1)\in \mathbb N$, this condition is equivalent to the global Markov c
期刊介绍:
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.