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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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