Pointwise convergence of averages along cubes
Abstract
Description
Let $(X,\mathcal{B},μ, T)$ be a measure preserving system. We prove the pointwise convergence of the averages $$\frac{1}{N^2}\sum_{n,m= 0}^{N-1} f_1(T^nx)f_2(T^mx)f_3(T^{n+m}x)$$ and of similar averages with seven bounded functions.
18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a reference
18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a reference