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Proceedings of the American Mathematical Society

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Convergence of weighted polynomial multiple ergodic averages

Author: Qing Chu
Journal: Proc. Amer. Math. Soc. 137 (2009), 1363-1369
MSC (2000): Primary 37A05, 37A30
Published electronically: October 16, 2008
MathSciNet review: 2465660
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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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Qing Chu
Affiliation: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050, 5 bd Descartes, 77454 Marne la Vallée Cedex 2, France

Keywords: Weighted ergodic averages, universally good sequences, Wiener-Wintner ergodic theorem, nilsequences
Received by editor(s): February 21, 2008
Received by editor(s) in revised form: April 14, 2008
Published electronically: October 16, 2008
Communicated by: Bryna Kra
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.