Existence of discrete ergodic singular transforms for admissible processes

• Autorzy: Doğan Çömez
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A99: None of the above, but in this section
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 2
• Strony: 335-343

Daty

wydano

2008

Twórcy

autor

Doğan Çömez

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

Identyfikatory

DOI

10.4064/cm112-2-8