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

2021/08/04 by Paulo M. Carvalho-Neto, Carvalho-Neto, Paulo Mendes, Renato Fehlberg Júnior +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #26A33 #46B50 #47G10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2108.02291

openalex publication_date 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Riemann-Liouville fractional integral of order α>0 as a linear operator from L^p(I,X) into itself, when 1≤ p≤ ∞, I=[t₀,t₁] (or I=[t₀,∞)) and X is a Banach space. In particular, when I=[t₀,t₁], we obtain necessary and sufficient conditions to ensure its compactness. We also prove that Riemann-Liouville fractional integral defines a C₀-semigroup but does not defines a uniformly continuous semigroup. We close this study by presenting lower and higher bounds to the norm of this operator.

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