{"title":"A Review on the Lebesgue Spaces","authors":"Santosh Ghimire, Bimala Mishra","doi":"10.3126/jsce.v9i9.46293","DOIUrl":null,"url":null,"abstract":"In this article, we begin with classical Lebesgue spaces Lp with p being constant and review the various properties such as completeness and duality of the space. To this end, we also discuss the boundedness of Hardy-Littlewood maximal function and interpolation on such spaces. Finally, we focus our attention on variable exponent Lebesgue spaces and review various results on it. Moreover, we also see the differences in between these Lebesgue spaces.","PeriodicalId":36368,"journal":{"name":"AIUB Journal of Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIUB Journal of Science and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3126/jsce.v9i9.46293","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: 0
Abstract
In this article, we begin with classical Lebesgue spaces Lp with p being constant and review the various properties such as completeness and duality of the space. To this end, we also discuss the boundedness of Hardy-Littlewood maximal function and interpolation on such spaces. Finally, we focus our attention on variable exponent Lebesgue spaces and review various results on it. Moreover, we also see the differences in between these Lebesgue spaces.
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