Pointwise multiple averages for systems with two commuting transformations

Sebastian Donoso, Wenbo Sun

We show that if $(X,\mathcal{X},\mu ,S,T)$ is an ergodic measure preserving system with commuting transformations $S$ and $T$, then the average \[\frac{1}{N^3} \sum_{i,j,k=0}^{N-1} f_…