Multiparameter Abelian ergodic theorems of Chacon–Báez–Duarte type

Abstract

We prove a multiparameter Llogk L generalization of the Baez– Duarte Abelian ergodic theorem for positive linear contractions on L1, which allows the application of the local convergence principle of Sucheston’s type. Next we establish a new weighted Abelian ratio ergodic theorem for Dunford– Schwartz operators on L1 with modulation by Besicovitch sequences. Moreover, this (one-parameter) result is generalized to the case of multiparameter operator averages, which allows the application of Fava’s maximal ergodic inequality.