JOP's counting function and Jones' square function
Volume 172 / 2006
Studia Mathematica 172 (2006), 1-23
MSC: Primary 42B25; Secondary 40A30.
DOI: 10.4064/sm172-1-1
Abstract
We study a class of square functions in a general framework with applications to a variety of situations: samples along subsequences, averages of $\mathbb Z_+^d$ actions and of positive $L^1$ contractions. We also study the relationship between a counting function first introduced by Jamison, Orey and Pruitt, in a variety of situations, and the corresponding ergodic averages. We show that the maximal counting function is not dominated by the square functions.
