New York Journal of Mathematics
Volume 12 (2006) 19-37


Parthena Avramidou

On certain weighted moving averages and their differentiation analogues

Published: April 3, 2006
Keywords: ergodic theory, differentiation
Subject: Primary 28D99,37A45; Secondary 47B38

Let (X,Σ,μ,T) be a measure-preserving dynamical system, and {In} a sequence of intervals of nonnegative integers moving to infinity with increasing cardinality. Rosenblatt and Wierdl constructed optimal weights wn for the averages of the form
(1/wn)∑k∈ Inf∘ Tk
to converge a.e. in L1. In this paper, we provide modified versions of those weights to address the question of optimality for more general weighted averages and their differentiation analogues.

Author information

Department of Mathematics, Ohio State University, Columbus, Ohio 43210