Convergence of weighted polynomial multiple ergodic averages

Chu, Qing

doi:10.1090/S0002-9939-08-09614-7

Convergence of weighted polynomial multiple ergodic averages
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Proc. Amer. Math. Soc. 137 (2009), 1363-1369 Request permission

Abstract:

In this article we study 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 covered by Host and Kra.

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