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.

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