New York Journal of Mathematics
Volume 17 (2011) 233-250


Paul Hagelstein and Alexander Stokolos

Weak type inequalities for maximal operators associated to double ergodic sums

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Published: March 16, 2011
Keywords: Multiparameter ergodic averages, multiparameter ergodic maximal operators
Subject: Primary 42B15, 42B25

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.


P. A. Hagelstein's research was partially supported by the Baylor University Research Leave Program.

Author information

Paul Hagelstein:
Department of Mathematics, Baylor University, Waco, Texas 76798

Alexander Stokolos:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia 30460-8093