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Iterating Bilinear Hardy Inequalities

Part of: Inequalities Linear function spaces and their duals Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  30 January 2017

Martin Křepela
Martin Křepela*
Affiliation:
Karlstad University, Faculty of Health, Science and Technology, Department of Mathematics and Computer Science, 651 88 Karlstad, Sweden (martin.krepela@kau.se) Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic
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Abstract

An iteration technique for characterizing boundedness of certain types of multilinear operators is presented, reducing the problem to a corresponding linear-operator case. The method gives a simple proof of a characterization of validity of the weighted bilinear Hardy inequality

for all non-negative f, g on (a, b), for 1 < p 1, p 2, q < ∞. More equivalent characterizing conditions are presented.

The same technique is applied to various further problems, in particular those involving multilinear integral operators of Hardy type.

Keywords

Hardy operatorsbilinear operatorsweightsoperator inequalities

MSC classification

Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 47G10: 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 Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 955 - 971
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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