Ergodic transforms associated to general averages

Tom 199 / 2010

H. Aimar, A. L. Bernardis, F. J. Martín-Reyes 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
    Facultad de Ciencias
    Universidad de Málaga
    29071 Málaga, Spain
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek