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On the lack of dimension-free estimates in Lp for maximal functions associated to radial measures

Published online by Cambridge University Press:  21 May 2010

Alberto Criado
Alberto Criado
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain (alberto.criado@uam.es)
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Abstract

In a recent article Aldaz proved that the weak L1 bounds for the centred maximal operator associated to finite radial measures cannot be taken independently with respect to the dimension. We show that the same result holds for the Lp bounds of such measures with decreasing densities, at least for small p near to one. We also give some concrete examples, including the Gaussian measure, where better estimates with respect to the general case are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 3 , June 2010 , pp. 541 - 552
Copyright
Copyright © Royal Society of Edinburgh 2010

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