New York Journal of Mathematics
Volume 3A (1997-1998) 31-67


Roger L. Jones

Ergodic Theory and Connections with Analysis and Probability

Published: December 17, 1997
Keywords: almost everywhere convergence, ergodic averages, strong sweeping out, convolution powers, oscillation inequalities, jump inequalities, variational inequalities, maximal functions, square functions, Calderón-Zygmund decomposition, Bourgain's entropy theorem
Subject: Primary: 28D05, 42B20; Secondary: 40A05, 42A50, 42B25, 60G42

In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis. We discuss divergence of operators, including strong sweeping out and Bourgain's entropy method. We consider square functions, oscillation operators, and variational operators for ergodic averages. We also consider almost everywhere convergence of convolution powers.


R. Jones is partially supported by NSF Grant DMS-9531526
This paper is based on a series of three talks given at the New York Journal of Mathematics Conference, which was held at Albany, N.Y. from June 9 - June 14, 1997.

Author information

Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago IL 60614