Existence of discrete ergodic singular transforms for admissible processes

Volume 112 / 2008

Doğan Çömez Colloquium Mathematicum 112 (2008), 335-343 MSC: Primary 28D05; Secondary 37A99, 42B20. DOI: 10.4064/cm112-2-8


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.


  • Doğan ÇömezDepartment of Mathematics
    North Dakota State University
    Fargo, ND 58105-5075, U.S.A.

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