Weak Type Inequalities for Maximal Operators Associated to Double Ergodic Sums

Authors

Paul Hagelstein, Baylor UniversityFollow
Alexander M. Stokolos, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

3-16-2011

Publication Title

New York Journal of Mathematics

ISSN

1076-9803

Abstract

Given an approach region Γ ∈ Z₊² and a pair U, V of commuting nonperiodic measure preserving transformations on a probability space (Ω, Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L¹(Ω) converge a.e. or that, given a positive increasing function ϕ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lϕ(L)(Ω) whose associated multiparameter ergodic averages fail to converge a.e.

Comments

This paper was retrieved from the New York Journal of Mathematics. Authors retain copyright of their work after publication.

Recommended Citation

Hagelstein, Paul, Alexander M. Stokolos. 2011. "Weak Type Inequalities for Maximal Operators Associated to Double Ergodic Sums." New York Journal of Mathematics, 17 (3-4): 233-250. source: http://nyjm.albany.edu/j/2011/17-11.html
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/189