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

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.

Locations

• Ergodic Theory and Dynamical Systems - View
• arXiv (Cornell University) - View - PDF
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