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arXiv · 2112.02669

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

Paulo Mendes Carvalho-Neto·Renato Fehlberg Júnior
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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 $1\leq q\leq p/(1-p\alpha)$, whether $I=[t_0,t_1]$ or $I=[t_0,\infty)$ and $X$ is a Banach space. Our main result give 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 $1\leq q< p/(1-p\alpha)$.

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Paulo Mendes Carvalho-Neto, Renato Fehlberg Júnior. 2021-12-05. The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II. https://arxiv.org/abs/2112.02669

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