Geodesic
Maximal inequality and ergodic theorems for Markov groups
Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 33-48

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper shows that for actions of Markov semigroups, in particular, of finitely generated word hyperbolic groups, the Cesàro means of spherical averages converge almost everywhere for any function from the class $L^p$, $p>1$. 
@article{TRSPY_2012_277_a2,
     author = {A. I. Bufetov and A. V. Klimenko},
     title = {Maximal inequality and ergodic theorems for {Markov} groups},
     journal = {Informatics and Automation},
     pages = {33--48},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a2/}
}
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A. I. Bufetov; A. V. Klimenko. Maximal inequality and ergodic theorems for Markov groups. Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 33-48. http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a2/