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
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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