Adell, José A.Gallardo Gutiérrez, Eva Antonia2023-06-202023-06-202007Adell, J. A. & Gallardo Gutiérrez, E. A. «The Norm of the Riemann-Liouville Operator on L p [0,1]: A Probabilistic Approach». Bulletin of the London Mathematical Society, vol. 39, n.o 4, agosto de 2007, pp. 565-74. DOI.org (Crossref), https://doi.org/10.1112/blms/bdm041.1469-212010.1112/blms/bdm041https://hdl.handle.net/20.500.14352/50600We obtain explicit lower and upper bounds for the norm of the Riemann-Liouville operator V-s on L-p[0, 1] which are asymptotically sharp, thus completing previous results by Eveson. Similar statements are shown with respect to the norms parallel to V-s f parallel to(p), whenever f satisfies certain smoothness properties. It turns out that the correct rate of convergence of parallel to V-s f parallel to(p) as s -> infinity depends both on the infimum of the support of f and on the degree of smoothness of f. We use a probabilistic approach which allows us to give unified proofs.engjournal articlehttps//doi.org/10.1112/blms/bdm041http://blms.oxfordjournals.org/content/39/4/565.full.pdf+htmlrestricted access517VOLTERRA OPERATORSAnálisis matemático1202 Análisis y Análisis Funcional