Convergence of weighted polynomial multiple ergodic averages

2008/02/21 by Qing Chu, Chu, Qing
Mathematics · #37A05 #37A30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A05 #msc:37A30

paper · pdf · doi:10.48550/arxiv.0802.3138

arxiv created 2008/11/24 · arxiv updated 2009/12/01

Abstract

We study here weighted polynomial multiple ergodic averages. A sequence of weights is called universally good if any polynomial multiple ergodic average with this sequence of weights converges in L². We find a necessary condition and show that for any bounded measurable function ϕ on an ergodic system, the sequence ϕ(Tⁿx) is universally good for almost every x. The linear case was understood by Host and Kra.

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