%0 Journal Article
%A Adell, José A.
%A Gallardo Gutiérrez, Eva Antonia
%T The norm of the Riemann-Liouville operator on L-p[0,1]: A probabilistic approach
%D 2007
%@ 1469-2120
%U https://hdl.handle.net/20.500.14352/50600
%X We 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.
%~