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Adell, José A. and Gallardo Gutiérrez, Eva A. (2007) The norm of the Riemann-Liouville operator on L-p[0,1]: A probabilistic approach. Bulletin of the London Mathematical Society, 39 (4). pp. 565-574. ISSN 1469-2120
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Official URL: http://blms.oxfordjournals.org/content/39/4/565.full.pdf+html
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.
Item Type: | Article |
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Uncontrolled Keywords: | VOLTERRA OPERATORS |
Subjects: | Sciences > Mathematics > Mathematical analysis |
ID Code: | 21068 |
Deposited On: | 25 Apr 2013 09:20 |
Last Modified: | 02 Aug 2018 08:38 |
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