Pointwise Convergence of Ergodic Averages in Orlicz Spaces
Dynamical Systems
2009-10-19 v2 Functional Analysis
Abstract
We show that for each Orlicz space properly contained in L^1 there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f in L^1. This extends the work of K. Reinhold, who, building on the work of A. Bellow,constructed a sequence for which the averages converge a.e. for every f in L^p, p>q, but diverge for some f in L^q. Our method, introduced by Bellow and extended by Reinhold and M. Wierdl, is perturbation.
Cite
@article{arxiv.0902.4645,
title = {Pointwise Convergence of Ergodic Averages in Orlicz Spaces},
author = {Andrew Parrish},
journal= {arXiv preprint arXiv:0902.4645},
year = {2009}
}