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

被引：3

作者：

Neto, Paulo Mendes Carvalho ^{[1
]}

Junior, Renato Fehlberg ^{[2
]}

机构：

[1] Univ Fed Santa Catarina, Dept Math, Florianopolis, SC, Brazil

[2] Univ Fed Espirito Santo, Dept Math, Vitoria, ES, Brazil

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2024年 / 27卷 / 03期

关键词：

Riemann-Liouville fractional integral; Hardy-Littlewood Theorem; Bochner-Lebesgue space; Bounded operator; Compact operators;

D O I：

10.1007/s13540-024-00255-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study the Riemann-Liouville fractional integral of order a is an element of(0, 1/p) as an operator from L-p(I; X) into L-q (I; X), with 1 <= q <= p/(1-p alpha), whether I = [t(0), t(1)] or I = [t(0), infinity) 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 <= q < p/(1 - p alpha).

引用

页码：1348 / 1368

页数：21

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