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Ergodic transforms associated to general averages

H. AimarA. L. BernardisF. J. Martín-Reyes — 2010

Studia Mathematica

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...

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