{"title":"单位球中调和函数的加权空间","authors":"A. Petrosyan, K. Avetisyan","doi":"10.46991/pysu:a/2017.51.1.003","DOIUrl":null,"url":null,"abstract":"We introduce the Banach spaces $h_{\\infty}(\\varphi)$, $h_{0}(\\varphi)$ and $h^{1}(\\psi)$ functions harmonic in the unit ball $B\\subset\\mathbb{R}^n$. These spaces depend on weight functions $\\varphi$, $\\psi$. We prove that if $\\varphi$ and $\\psi$ form a normal pair, then $h^{1}(\\psi)^*\\sim h_{\\infty}(\\varphi)$ and $h_{0}(\\varphi)^*\\sim h^{1}(\\psi)$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL\",\"authors\":\"A. Petrosyan, K. Avetisyan\",\"doi\":\"10.46991/pysu:a/2017.51.1.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the Banach spaces $h_{\\\\infty}(\\\\varphi)$, $h_{0}(\\\\varphi)$ and $h^{1}(\\\\psi)$ functions harmonic in the unit ball $B\\\\subset\\\\mathbb{R}^n$. These spaces depend on weight functions $\\\\varphi$, $\\\\psi$. We prove that if $\\\\varphi$ and $\\\\psi$ form a normal pair, then $h^{1}(\\\\psi)^*\\\\sim h_{\\\\infty}(\\\\varphi)$ and $h_{0}(\\\\varphi)^*\\\\sim h^{1}(\\\\psi)$.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.1.003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.1.003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL
We introduce the Banach spaces $h_{\infty}(\varphi)$, $h_{0}(\varphi)$ and $h^{1}(\psi)$ functions harmonic in the unit ball $B\subset\mathbb{R}^n$. These spaces depend on weight functions $\varphi$, $\psi$. We prove that if $\varphi$ and $\psi$ form a normal pair, then $h^{1}(\psi)^*\sim h_{\infty}(\varphi)$ and $h_{0}(\varphi)^*\sim h^{1}(\psi)$.
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