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Convergence of weighted polynomial multiple ergodic averages

Authors :
Chu, Qing
Publication Year :
2008

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 $L^{2}$. We find a necessary condition and show that for any bounded measurable function $\phi$ on an ergodic system, the sequence $\phi(T^{n}x)$ is universally good for almost every $x$. The linear case was understood by Host and Kra.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.0802.3138
Document Type :
Working Paper