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- 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.
