Pointwise convergence of some multiple ergodic averages

Sebastián Donoso, Wenbo Sun

We show that for every ergodic system $(X,\mu ,T_1,\dots ,T_d)$ with commuting transformations, the average \[\frac{1}{N^{d+1}} \sum_{0\leq n_1,\ldots,n_d \leq N-1} \sum_{0\leq n\leq…