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Pré-Publication, Document De Travail Année : 2008

Convergence of weighted polynomial multiple ergodic averages

Résumé

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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Dates et versions

hal-00257899 , version 1 (21-02-2008)
hal-00257899 , version 2 (24-11-2008)

Identifiants

Citer

Qing Chu. Convergence of weighted polynomial multiple ergodic averages. 2008. ⟨hal-00257899v2⟩
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