Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups

Abstract

Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\le p<\infty$, and pointwise convergence for functions in $L^{\infty }$. 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.

arXiv comment32 pages

References in corpus (1)

• A pointwise ergodic theorem for Fuchsian groups