Convergence of weighted polynomial multiple ergodic averages

Details Convergence of weighted polynomial multiple ergodic averages Convergence of weighted polynomial multiple ergodic averages

2008-02-21

arxiv.org/abs/0802.3138v2

Mathematics

Dynamical Systems

Scientific paper

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.

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