{"title":"Compact imbedding theorems in Musielak spaces","authors":"Youssef Ahmida, Ahmed Youssfi","doi":"10.1007/s43034-025-00410-y","DOIUrl":null,"url":null,"abstract":"<div><p>We provide compact imbedding results for Musielak–Sobolev spaces built on smooth bounded domains from Musielak functions, on which we impose, among others, natural integral conditions that extend those used in the framework of Orlicz spaces. We obtain the Rellich–Kondrachov theorem for regular Musielak functions. We then apply the results obtained to get a Poincaré-type inequality in Musielak spaces, which we use to solve a class of nonlinear elliptic problems.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-025-00410-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We provide compact imbedding results for Musielak–Sobolev spaces built on smooth bounded domains from Musielak functions, on which we impose, among others, natural integral conditions that extend those used in the framework of Orlicz spaces. We obtain the Rellich–Kondrachov theorem for regular Musielak functions. We then apply the results obtained to get a Poincaré-type inequality in Musielak spaces, which we use to solve a class of nonlinear elliptic problems.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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