We study a class of square functions in a general framework with applications to a variety of situations: samples along subsequences, averages of actions and of positive L¹ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-1,
author = {Karin Reinhold},
title = {JOP's counting function and Jones' square function},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {1-23},
zbl = {1113.42017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-1}
}
Karin Reinhold. JOP's counting function and Jones' square function. Studia Mathematica, Tome 173 (2006) pp. 1-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-1/