Weighted maximal functions and derivatives of invariant Poisson integrals of potentials

Patrick Robert Ahern and William S. Cohn

Vol. 163 (1994), No. 1, 1–16

DOI: 10.2140/pjm.1994.163.1

Abstract

In this paper we prove L^p estimates for weighted maximal functions of invariant Poisson integrals of potentials. From this it follows that the exceptional sets of the Poisson integrals of potentials are sets of zero Hausdorff capacity.

Mathematical Subject Classification 2000

Primary: 42B30

Secondary: 32A35, 42B25, 47B38

Milestones

Received: 1 December 1991

Published: 1 March 1994