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

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

2009-07-24

arxiv.org/abs/0907.4326v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In a recent article J. Aldaz proved that the weak L1 bounds for the centered maximal operator associated to finite radial measures cannot be taken independently with respect to the dimension. We show that at least for small p near to 1 the same result holds for the Lp bounds of such measures with decreasing densities. We also give some concrete examples, that include Gaussian measure, where better estimates with respect to the general case are obtained.

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