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One-dimensional Hardy-type inequalities in many dimensions

Published online by Cambridge University Press:  14 November 2011

Gord Sinnamon
Gord Sinnamon
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada e-mail: sinnamon@uwo.ca
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Abstract

Weighted inequalities for certain Hardy-type averaging operators in are shown to be equivalent to weighted inequalities for one-dimensional operators. Known results for the one-dimensional operators are applied to give weight characterisations, with best constants in some cases, in the higher-dimensional setting. Operators considered include averages over all dilations of very general starshaped regions as well as averages over all balls touching the origin. As a consequence, simple weight conditions are given which imply weighted norm inequalities for a class of integral operators with monotone kernels.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 833 - 848
Copyright
Copyright © Royal Society of Edinburgh 1998

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