{"title":"TWO-WEIGHTED ESTIMATES OF RIEMANN-LIOUVILLE INTEGRALS","authors":"V. Stepanov","doi":"10.1070/IM1991V036N03ABEH002039","DOIUrl":null,"url":null,"abstract":"Weighted estimates (1)are considered, where the constant does not depend on , for fractional Riemann- Liouville integrals and the following problem is examined: find necessary and sufficient conditions on weight functions and under which estimate (1) is valid for all functions for which the right-hand side of (1) is finite. The problem is solved for and . This result is definitive, and it generalizes known results for integral operators when . Bibliography: 19 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"58","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V036N03ABEH002039","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 58
Abstract
Weighted estimates (1)are considered, where the constant does not depend on , for fractional Riemann- Liouville integrals and the following problem is examined: find necessary and sufficient conditions on weight functions and under which estimate (1) is valid for all functions for which the right-hand side of (1) is finite. The problem is solved for and . This result is definitive, and it generalizes known results for integral operators when . Bibliography: 19 titles.
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