{"title":"加权狄利克雷型空间中多项式的密度","authors":"A. Abkar","doi":"10.30495/JME.V0I0.1771","DOIUrl":null,"url":null,"abstract":"We study weighted Dirichlet type spaces in the unit disk. We prove that analytic polynomials are dense in weighted Dirichlet type spaces if the (non-radial) weight function is super-biharmonic and satisfies a growth condition up to the boundary.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Density of polynomials in certain weighted Dirichlet type spaces\",\"authors\":\"A. Abkar\",\"doi\":\"10.30495/JME.V0I0.1771\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study weighted Dirichlet type spaces in the unit disk. We prove that analytic polynomials are dense in weighted Dirichlet type spaces if the (non-radial) weight function is super-biharmonic and satisfies a growth condition up to the boundary.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.1771\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1771","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Density of polynomials in certain weighted Dirichlet type spaces
We study weighted Dirichlet type spaces in the unit disk. We prove that analytic polynomials are dense in weighted Dirichlet type spaces if the (non-radial) weight function is super-biharmonic and satisfies a growth condition up to the boundary.