Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T19:54:12.316Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)