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Optimal rearrangement invariant range for Hardy-type operators

Part of: Linear function spaces and their duals Inequalities

Published online by Cambridge University Press:  12 May 2016

Javier Soria  and
Pedro Tradacete
Javier Soria
Affiliation:
Department of Mathematics and Informatics, University of Barcelona, Gran Via 585, 08007 Barcelona, Spain (soria@ub.edu)
Pedro Tradacete
Affiliation:
Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain (ptradace@math.uc3m.es)
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Extract

We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between the optimal range and the optimal domain for these operators is carefully analysed.

Keywords

rearrangement invariant spacesrestricted typeHardy operatoroptimal rangeoptimal domain

MSC classification

Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 4 , August 2016 , pp. 865 - 893
Copyright
Copyright © Royal Society of Edinburgh 2016 

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