IMAL 13325
INSTITUTO DE MATEMATICA APLICADA DEL LITORAL "DRA. ELEONOR HARBOURE"
Unidad Ejecutora - UE
artículos
Título:
Ergodic transforms associated to general averages
Autor/es:
AIMAR, HUGO; BERNARDIS, ANA, MARTIN-REYES, FRANCISCO
Revista:
STUDIA MATHEMATICA
Editorial:
POLISH ACAD SCIENCES INST MATHEMATICS
Referencias:
Año: 2010 vol. 199 p. 107 - 143
ISSN:
0039-3223
Resumen:
Abstract. Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a uni ed treatment of the ergodic transforms associated to positive groups induced by nonsingular ows and to general means which include the usual averages, Cesaro-averages and Abel means. We prove the boundedness in Lp, 1 < p < 1, of the maximal ergodic transforms assuming that the semigroup is Cesaro bounded in Lp. For p = 1 we nd that the maximal ergodic transforms are of weak type (1; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a uni ed treatment of the ergodic transforms associated to positive groups induced by nonsingular ows and to general means which include the usual averages, Cesaro-averages and Abel means. We prove the boundedness in Lp, 1 < p < 1, of the maximal ergodic transforms assuming that the semigroup is Cesaro bounded in Lp. For p = 1 we nd that the maximal ergodic transforms are of weak type (1; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.averages and Abel means. We prove the boundedness in Lp, 1 < p < 1, of the maximal ergodic transforms assuming that the semigroup is Cesaro bounded in Lp. For p = 1 we nd that the maximal ergodic transforms are of weak type (1; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.Lp, 1 < p < 1, of the maximal ergodic transforms assuming that the semigroup is Cesaro bounded in Lp. For p = 1 we nd that the maximal ergodic transforms are of weak type (1; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.Lp. For p = 1 we nd that the maximal ergodic transforms are of weak type (1; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.; 1). Convergence results are also proved. We give some general examples of Cesaro bounded semigroups.
