# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Ergodic transforms associated to general averages

### Tom 199 / 2010

Studia Mathematica 199 (2010), 107-143 MSC: 47A35, 37A40, 42B25. DOI: 10.4064/sm199-2-1

#### Streszczenie

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.

#### Autorzy

• H. AimarIMAL-CONICET
Güemes 3450
3000 Santa Fe, Argentina
e-mail
• A. L. BernardisIMAL-CONICET
Güemes 3450
3000 Santa Fe, Argentina
e-mail
• F. J. Martín-ReyesDepartamento
de Análisis Matemático
29071 Málaga, Spain
e-mail

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