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Tr. Mat. Inst. Steklova, 2012, Volume 277, Pages 33–48 (Mi tm3382)  
This article is cited in 2 scientific papers (total in 2 papers)

Maximal inequality and ergodic theorems for Markov groups

A. I. Bufetovabc, A. V. Klimenkoab

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia

Abstract: 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 $L^p$, $p>1$.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00654
10-01-93115
Ministry of Education and Science of the Russian Federation NSh-8508.2010.1
MK-4893.2010.1
MK-6734.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Dynasty Foundation
Simons Foundation
Alfred P. Sloan Foundation
This work was partially supported by the Russian Foundation for Basic Research (project no. 11-01-00654), RFBR-CNRS (project no. 10-01-93115), by grants of the President of the Russian Federation (project nos. NSh-8508.2010.1, MK-4893.2010.1, and MK-6734.2012.1), and by the program "Mathematical Control Theory" of the Presidium of the Russian Academy of Sciences. A.B. is Alfred P. Sloan Research Fellow, Dynasty Foundation Fellow, and IUM-Simons Fellow.


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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 277, 27–42

Bibliographic databases:

UDC: 517.987.5
Received in January 2012

Citation: A. I. Bufetov, A. V. Klimenko, “Maximal inequality and ergodic theorems for Markov groups”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 33–48; Proc. Steklov Inst. Math., 277 (2012), 27–42

Citation in format AMSBIB
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\by A.~I.~Bufetov, A.~V.~Klimenko
\paper Maximal inequality and ergodic theorems for Markov groups
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 33--48
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3052262}
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\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 277
\pages 27--42
\crossref{https://doi.org/10.1134/S0081543812040037}
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    This publication is cited in the following articles:
    1. Bowen L., Nevo A., “Von Neumann and Birkhoff Ergodic Theorems For Negatively Curved Groups”, Ann. Sci. Ec. Norm. Super., 48:5 (2015), 1113–1147  crossref  mathscinet  zmath  isi
    2. Bowen L., Nevo A., “Amenable Equivalence Relations and the Construction of Ergodic Averages For Group Actions”, J. Anal. Math., 126:1 (2015), 359–388  crossref  mathscinet  zmath  isi  elib  scopus
    		• Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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