Jones and
Rosenblatt started the study of an ergodic transform which is
analogous to the martingale transform. In this paper we present a
unified treatment of the ergodic transforms associated to positive
groups induced by
nonsingular flows and to general means which include the usual
averages, Cesàro-$\alpha$ averages and Abel means. We prove the
boundedness in $L^p$, $1 p \infty$, of the maximal ergodic
transforms assuming that the semigroup is Cesàro bounded in
$L^p$. For $p=1$ we find that the maximal ergodic transforms are
of weak type $(1,1)$. Convergence results are also proved. We give
some general examples of Cesàro bounded semigroups.
Keywords:
jones rosenblatt started study ergodic transform which analogous martingale transform paper present unified treatment ergodic transforms associated positive groups induced nonsingular flows general means which include usual averages ces ro alpha averages abel means prove boundedness infty maximal ergodic transforms assuming semigroup ces bounded maximal ergodic transforms weak type convergence results proved general examples ces bounded semigroups
Affiliations des auteurs :
H. Aimar
1
;
A. L. Bernardis
1
;
F. J. Martín-Reyes
2
1
IMAL-CONICET Güemes 3450 3000 Santa Fe, Argentina
2
Departamento de Análisis Matemático Facultad de Ciencias Universidad de Málaga 29071 Málaga, Spain
@article{10_4064_sm199_2_1,
author = {H. Aimar and A. L. Bernardis and F. J. Mart{\'\i}n-Reyes},
title = {Ergodic transforms associated to general averages},
journal = {Studia Mathematica},
pages = {107--143},
year = {2010},
volume = {199},
number = {2},
doi = {10.4064/sm199-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm199-2-1/}
}
TY - JOUR
AU - H. Aimar
AU - A. L. Bernardis
AU - F. J. Martín-Reyes
TI - Ergodic transforms associated to general averages
JO - Studia Mathematica
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SP - 107
EP - 143
VL - 199
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%J Studia Mathematica
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H. Aimar; A. L. Bernardis; F. J. Martín-Reyes. Ergodic transforms associated to general averages. Studia Mathematica, Tome 199 (2010) no. 2, pp. 107-143. doi: 10.4064/sm199-2-1
