Publication: The norm of the Riemann-Liouville operator on L-p[0,1]: A probabilistic approach
Loading...
Full text at PDC
Publication Date
2007
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
London Mathematical Society
Citations
Exportar
Abstract
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.