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arXiv · 1405.3499

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

Vjekoslav Kovač
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Abstract

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

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Vjekoslav Kovač. 2015-02-02. Quantitative norm convergence of double ergodic averages associated with two commuting group actions. https://doi.org/10.1017/etds.2014.87

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