Existence of discrete ergodic singular transforms for admissible processes

Doğan Çömez¹

¹ Department of Mathematics North Dakota State University Fargo, ND 58105-5075, U.S.A.

Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 335-343.

Résumé

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.

Détail

DOI : 10.4064/cm112-2-8

Keywords: article concerned study discrete version generalized ergodic calder zygmund singular operators shown discrete ergodic singular operators class superadditive processes namely bounded symmetric admissible processes relative measure preserving transformations weak maximal inequality existence discrete ergodic singular transform obtained superadditive processes generalizes well known result existence ergodic hilbert transform