{"title":"Bochner-Lebesgue 空间中的黎曼-刘维尔分数积分 II","authors":"","doi":"10.1007/s13540-024-00255-7","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this work we study the Riemann-Liouville fractional integral of order <span> <span>\\(\\alpha \\in (0,1/p)\\)</span> </span> as an operator from <span> <span>\\(L^p(I;X)\\)</span> </span> into <span> <span>\\(L^{q}(I;X)\\)</span> </span>, with <span> <span>\\(1\\le q\\le p/(1-p\\alpha )\\)</span> </span>, whether <span> <span>\\(I=[t_0,t_1]\\)</span> </span> or <span> <span>\\(I=[t_0,\\infty )\\)</span> </span> and <em>X</em> is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from <span> <span>\\(L^p(t_0,t_1;X)\\)</span> </span> into <span> <span>\\(L^{q}(t_0,t_1;X)\\)</span> </span>, when <span> <span>\\(1\\le q< p/(1-p\\alpha )\\)</span> </span>.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II\",\"authors\":\"\",\"doi\":\"10.1007/s13540-024-00255-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>In this work we study the Riemann-Liouville fractional integral of order <span> <span>\\\\(\\\\alpha \\\\in (0,1/p)\\\\)</span> </span> as an operator from <span> <span>\\\\(L^p(I;X)\\\\)</span> </span> into <span> <span>\\\\(L^{q}(I;X)\\\\)</span> </span>, with <span> <span>\\\\(1\\\\le q\\\\le p/(1-p\\\\alpha )\\\\)</span> </span>, whether <span> <span>\\\\(I=[t_0,t_1]\\\\)</span> </span> or <span> <span>\\\\(I=[t_0,\\\\infty )\\\\)</span> </span> and <em>X</em> is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from <span> <span>\\\\(L^p(t_0,t_1;X)\\\\)</span> </span> into <span> <span>\\\\(L^{q}(t_0,t_1;X)\\\\)</span> </span>, when <span> <span>\\\\(1\\\\le q< p/(1-p\\\\alpha )\\\\)</span> </span>.</p>\",\"PeriodicalId\":48928,\"journal\":{\"name\":\"Fractional Calculus and Applied Analysis\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Calculus and Applied Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00255-7\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00255-7","RegionNum":2,"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
摘要
Abstract In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\) , with\(1\le q\le p/(1-p\alpha )\).with （1嘞 q嘞 p/(1-p\alpha )\)，无论是（I=[t_0,t_1]\）还是（I=[t_0,\infty )\），X 都是一个巴拿赫空间。我们的主要结果提供了必要条件和充分条件，以确保从 \(L^p(t_0,t_1;X)\) 到 \(L^{q}(t_0,t_1;X)\) 的黎曼-柳维尔分数积分的紧凑性。, when \(1\le q< p/(1-p\alpha )\) .
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II
Abstract
In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\), with \(1\le q\le p/(1-p\alpha )\), whether \(I=[t_0,t_1]\) or \(I=[t_0,\infty )\) and X is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from \(L^p(t_0,t_1;X)\) into \(L^{q}(t_0,t_1;X)\), when \(1\le q< p/(1-p\alpha )\).
期刊介绍：
Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
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