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

2021/12/05 by Carvalho-Neto, Paulo Mendes, Júnior, Renato Fehlberg · 2 citations
#26A33 #46B50 #47G10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2112.02669

Abstract

In this work we study the Riemann-Liouville fractional integral of order α∈(0,1/p) as an operator from L^p(I;X) into L^q(I;X), with 1≤ q≤ p/(1-pα), whether I=[t₀,t₁] or I=[t₀,∞) 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(t₀,t₁;X) into L^q(t₀,t₁;X), when 1≤ q< p/(1-pα).

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