Existence of discrete ergodic singular transforms for admissible processes
Tom 112 / 2008
Colloquium Mathematicum 112 (2008), 335-343
MSC: Primary 28D05; Secondary 37A99, 42B20.
DOI: 10.4064/cm112-2-8
Streszczenie
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.
