The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-02-26 DOI:10.1007/s13540-024-00255-7

引用次数: 0

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 \(1\le q< p/(1-p\alpha )\) .

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Bochner-Lebesgue 空间中的黎曼-刘维尔分数积分 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\(1\le q\le p/(1-p\alpha )\).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 \(1\le q< p/(1-p\alpha )\) .

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464