Venancio Alvarez, D. Pestana, José M. Rodríguez, Elena Romera
{"title":"Weighted Sobolev Spaces on Curves","authors":"Venancio Alvarez, D. Pestana, José M. Rodríguez, Elena Romera","doi":"10.1006/jath.2002.3709","DOIUrl":null,"url":null,"abstract":"In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"109 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Approx. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1006/jath.2002.3709","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 28
Abstract
In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.
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