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