Averages along cubes for not necessarily commuting measure preserving transformations

Details Averages along cubes for not necessarily commuting measure preserving transformations Averages along cubes for not necessarily commuting measure preserving transformations

2005-11-02

arxiv.org/abs/math/0511062v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

We study the pointwise convergence of some weighted averages linked to averages along cubes. We show that if $(X,\mathcal{B},\mu, T_i)$ are not necessarily commuting measure preserving systems on the same finite measure space and if $f_i,$ $1\leq i\leq 6$ are bounded functions then the averages $$\frac{1}{N^3}\sum_{n, m, p=1}^N f_1(T_1^nx) f_2(T_2^mx) f_3(T_3^px) f_4(T_4^{n+m}x) f_5(T_5^{n+p}x) f_6(T_6^{m+p}x)$$ converge almost everywhere.

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