{"title":"Composition operators on W1X are necessarily induced by quasiconformal mappings","authors":"L. Kleprlík","doi":"10.2478/s11533-013-0392-8","DOIUrl":null,"url":null,"abstract":"Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to Lq(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W1X to W1X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"53 1","pages":"1229-1238"},"PeriodicalIF":0.0000,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0392-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to Lq(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W1X to W1X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
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