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-α averages and Abel means. We prove the boundedness in , 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in . 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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {196},
year = {2010},
pages = {107-143},
zbl = {1217.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-2-1}
}
H. Aimar; A. L. Bernardis; F. J. Martín-Reyes. Ergodic transforms associated to general averages. Studia Mathematica, Tome 196 (2010) pp. 107-143. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-2-1/