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• # Artykuł - szczegóły

## Studia Mathematica

2010 | 199 | 2 | 107-143

## Ergodic transforms associated to general averages

EN

### Abstrakty

EN
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.

107-143

wydano
2010

### Twórcy

autor
• IMAL-CONICET, Güemes 3450, 3000 Santa Fe, Argentina
autor
• IMAL-CONICET, Güemes 3450, 3000 Santa Fe, Argentina
autor
• Departamento, de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain