Pointwise Convergence of Ergodic Averages in Orlicz Spaces

Details Pointwise Convergence of Ergodic Averages in Orlicz Spaces Pointwise Convergence of Ergodic Averages in Orlicz Spaces

2009-02-26

arxiv.org/abs/0902.4645v2

Mathematics

Dynamical Systems

Scientific paper

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.

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