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Abstract

This article is concerned with the study of the discrete version of generalized ergodic Calderón–Zygmund singular operators. It is shown that such discrete ergodic singular operators for a class of superadditive processes, namely, bounded symmetric admissible processes relative to measure preserving transformations, are weak $(1,1)$. From this maximal inequality, a.e. existence of the discrete ergodic singular transform is obtained for such superadditive processes. This generalizes the well-known result on the existence of the ergodic Hilbert transform.