Ergodic transforms associated to general averages

H. Aimar, A. L. Bernardis, and F. J. Martín-Reyes. "Ergodic transforms associated to general averages." Studia Mathematica 199.2 (2010): 107-143. <http://eudml.org/doc/285416>.

@article{H2010,
abstract = {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 $L^\{p\}$, 1 < p < ∞, 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.},
author = {H. Aimar, A. L. Bernardis, F. J. Martín-Reyes},
journal = {Studia Mathematica},
keywords = {ergodic transforms; averages; Cesàro averages; Abel means; weights; Cesàro bounded semigroups; weights; weighted inequalities},
language = {eng},
number = {2},
pages = {107-143},
title = {Ergodic transforms associated to general averages},
url = {http://eudml.org/doc/285416},
volume = {199},
year = {2010},
}

TY - JOUR
AU - H. Aimar
AU - A. L. Bernardis
AU - F. J. Martín-Reyes
TI - Ergodic transforms associated to general averages
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 2
SP - 107
EP - 143
AB - 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 $L^{p}$, 1 < p < ∞, 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.
LA - eng
KW - ergodic transforms; averages; Cesàro averages; Abel means; weights; Cesàro bounded semigroups; weights; weighted inequalities
UR - http://eudml.org/doc/285416
ER -