{"title":"Composition Operators in Grand Lebesgue Spaces","authors":"A. Karapetyants, M. Lanza de Cristoforis","doi":"10.1007/s10476-023-0201-y","DOIUrl":null,"url":null,"abstract":"<div><p>Let Ω be an open subset of ℝ<sup><i>n</i></sup> of finite measure. Let <i>f</i> be a Borel measurable function from ℝ to ℝ. We prove necessary and sufficient conditions on <i>f</i> in order that the composite function <i>T</i><sub><i>f</i></sub>[<i>g</i>] = <i>f</i> o <i>g</i> belongs to the Grand Lebesgue space <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω) whenever <i>g</i> belongs to <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω).</p><p>We also study continuity, uniform continuity, Hölder and Lipschitz continuity of the composition operator <i>T</i><sub><i>f</i></sub>[·] in <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω).</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 1","pages":"151 - 166"},"PeriodicalIF":0.6000,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0201-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let Ω be an open subset of ℝn of finite measure. Let f be a Borel measurable function from ℝ to ℝ. We prove necessary and sufficient conditions on f in order that the composite function Tf[g] = f o g belongs to the Grand Lebesgue space Lp),θ(Ω) whenever g belongs to Lp),θ(Ω).
We also study continuity, uniform continuity, Hölder and Lipschitz continuity of the composition operator Tf[·] in Lp),θ(Ω).
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
