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

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