{"title":"Characterizations for the fractional maximal operator and its commutators on total Morrey spaces","authors":"V. S. Guliyev","doi":"10.1007/s11117-024-01068-x","DOIUrl":null,"url":null,"abstract":"<p>We shall give a characterization for the strong and weak type Adams type boundedness of the fractional maximal operator <span>\\(M_{\\alpha }\\)</span> on total Morrey spaces <span>\\(L^{p,\\lambda ,\\mu }(\\mathbb {R}^n)\\)</span>, respectively. Also we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator <span>\\(M_{b,\\alpha }\\)</span> and commutator of fractional maximal operator <span>\\([b,M_{\\alpha }]\\)</span> on <span>\\(L^{p,\\lambda ,\\mu }(\\mathbb {R}^n)\\)</span> when <i>b</i> belongs to <span>\\(BMO(\\mathbb {R}^n)\\)</span> spaces, whereby some new characterizations for certain subclasses of <span>\\(BMO(\\mathbb {R}^n)\\)</span> spaces are obtained.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Positivity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11117-024-01068-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We shall give a characterization for the strong and weak type Adams type boundedness of the fractional maximal operator \(M_{\alpha }\) on total Morrey spaces \(L^{p,\lambda ,\mu }(\mathbb {R}^n)\), respectively. Also we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator \(M_{b,\alpha }\) and commutator of fractional maximal operator \([b,M_{\alpha }]\) on \(L^{p,\lambda ,\mu }(\mathbb {R}^n)\) when b belongs to \(BMO(\mathbb {R}^n)\) spaces, whereby some new characterizations for certain subclasses of \(BMO(\mathbb {R}^n)\) spaces are obtained.
期刊介绍:
The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome.
The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.