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Quantitative norm convergence of double ergodic averages associated with two commuting group actions

Published online by Cambridge University Press:  06 November 2014

VJEKOSLAV KOVAČ
VJEKOSLAV KOVAČ*
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia email vjekovac@math.hr
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Abstract

We study double averages along orbits for measure-preserving actions of $\mathbb{A}^{{\it\omega}}$, the direct sum of countably many copies of a finite abelian group $\mathbb{A}$. We show an $\text{L}^{p}$ norm-variation estimate for these averages, which in particular re-proves their convergence in $\text{L}^{p}$ for any finite $p$ and for any choice of two $\text{L}^{\infty }$ functions. The result is motivated by recent questions on quantifying convergence of multiple ergodic averages.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 860 - 874
Copyright
© Cambridge University Press, 2014 

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