Bounds for maximal functions associated with rotational invariant measures in high dimensions
Artikel i vetenskaplig tidskrift, 2014

ABSTRACT. In recent articles, it was proved that when mu is a finite, radial measure in Rn with a bounded, radially decreasing density, the Lp(mu) norm of the associated maximal operator grows to infinity with the dimension for a small range of values of p near 1. We prove that when mu is Lebesgue measure restricted to the unit ball and p < 2, the Lp operator norms of the maximal operator are unbounded in dimension, even when the action is restricted to radially decreasing functions. In spite of this, this maximal operator admits dimension-free Lp bounds for every p > 2, when restricted to radially decreasing functions. On the other hand, when mu is the Gaussian measure, the Lp operator norms of the maximal operator grow to infinity with the dimension for any finite p > 1, even in the subspace of radially decreasing functions.

Maximal functions

Radial measures

42B25

Dimension free estimates

Författare

Alberto Criado

Peter Sjögren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. 24 2 595-612

Ämneskategorier

Matematisk analys

DOI

10.1007/s12220-012-9346-9