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Статья

Cesàro Convergence of Spherical Averages for Measure-Preserving Actions of Markov Semigroups and Groups

International Mathematics Research Notices. 2012. No. 21. P. 4797-4829.
Khristoforov M., Klimenko A. V., Bufetov A. I.

Cesaro convergence of spherical averages is proven for measurepreserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in Lp, 1  p < 1, and pointwise convergence for functions in L1. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.