Ergodic transforms associated to general averages

• Autorzy: H. Aimar , A. L. Bernardis , F. J. Martín-Reyes
• Języki publikacji: 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.

Kategorie tematyczne

• 47A35: Ergodic theory
• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 2
• Strony: 107-143

Daty

wydano

2010

Twórcy

autor

H. Aimar

• IMAL-CONICET, Güemes 3450, 3000 Santa Fe, Argentina

autor

A. L. Bernardis

• IMAL-CONICET, Güemes 3450, 3000 Santa Fe, Argentina

autor

F. J. Martín-Reyes

• Departamento, de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

Identyfikatory

DOI

10.4064/sm199-2-1