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

Alexander I. Bufetov (1) , Mikhail Khristoforov (2) , Alexey Klimenko (3)

1 I2M - Institut de Mathématiques de Marseille
2 Chebyshev Laboratory
3 SMI | RAS - Steklov Mathematical Institute [Moscow]

Ces aro 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 ≤ p < ∞, and pointwise convergence for functions in L ∞. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Ces aro convergence of spherical averages with respect to any symmetric set of generators.

Domaines: Systèmes dynamiques [math.DS]

Alexander I. Bufetov, Mikhail Khristoforov, Alexey Klimenko. Cesàro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups. International Mathematics Research Notices, 2012. ⟨hal-01256198⟩