The maximal ergodic Hilbert transform with weights

Enrique Atencia and Francisco Javier Martin-Reyes

Vol. 108 (1983), No. 2, 257–263

DOI: 10.2140/pjm.1983.108.257

Abstract

This work is concerned with the characterization of those positive functions, w, such that the ergodic maximal Hilbert transform associated to an invertible, measure preserving, ergodic transformation on a probability space, is a bounded operator in L_p(wdμ).

Mathematical Subject Classification 2000

Primary: 28D05

Secondary: 42A50, 44A15, 47A35

Milestones

Received: 8 April 1981

Revised: 13 May 1982

Published: 1 October 1983