English

Pointwise convergence of averages along cubes

Dynamical Systems 2007-05-23 v2

Abstract

Let (X,B,μ,T)(X,\mathcal{B},\mu, T) be a measure preserving system. We prove the pointwise convergence of the averages 1N2n,m=0N1f1(Tnx)f2(Tmx)f3(Tn+mx)\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.

Keywords

Cite

@article{arxiv.math/0305388,
  title  = {Pointwise convergence of averages along cubes},
  author = {Idris Assani},
  journal= {arXiv preprint arXiv:math/0305388},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T16:54:54.176Z