AN EXPLICIT CHARACTERIZATION OF THE DOMAIN OF THE INFINITESIMAL GENERATOR OF A SYMMETRIC DIFFUSION SEMIGROUP ON LP OF A COMPLETE POSITIVE SIGMA-FINITE MEASURE SPACE
{"title":"AN EXPLICIT CHARACTERIZATION OF THE DOMAIN OF THE INFINITESIMAL GENERATOR OF A SYMMETRIC DIFFUSION SEMIGROUP ON LP OF A COMPLETE POSITIVE SIGMA-FINITE MEASURE SPACE","authors":"Maxim J. Goldberg, Seonja Kim","doi":"10.14321/REALANALEXCH.46.2.0345","DOIUrl":null,"url":null,"abstract":"Let X be a complete positive σ–finite measure space and {At}t≥0 be a symmetric diffusion semigroup of contraction operators on Lp(X). We prove that for 1<p<∞, the domain of the infinitesimal generator of the semigroup is precisely the space ∫01Ash ds:h∈Lp(X). We also establish that for 1<p<∞, the function spaces 2n-1∫02-(n-1)Ash ds|h∈Lp(X) are equal for every n∈ℤ.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Real Analysis Exchange","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14321/REALANALEXCH.46.2.0345","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Let X be a complete positive σ–finite measure space and {At}t≥0 be a symmetric diffusion semigroup of contraction operators on Lp(X). We prove that for 1
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