Pointwise convergence of averages along cubes

Details Pointwise convergence of averages along cubes Pointwise convergence of averages along cubes

2003-05-27

arxiv.org/abs/math/0305388v2

Mathematics

Dynamical Systems

18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a reference

Scientific paper

Let $(X,\mathcal{B},\mu, T)$ 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.

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