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Paul Hagelstein and Alexander Stokolos
Weak type inequalities for maximal operators associated to double ergodic sums view print
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| Published: |
March 16, 2011 |
| Keywords: |
Multiparameter ergodic averages, multiparameter ergodic maximal operators |
| Subject: |
Primary 42B15, 42B25 |
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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.
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| Acknowledgements
P. A. Hagelstein's research was partially supported by the Baylor University Research Leave Program.
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| Author information
Paul Hagelstein:
Department of Mathematics, Baylor University, Waco, Texas 76798
paul_hagelstein@baylor.edu
Alexander Stokolos:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia 30460-8093
astokolos@georgiasouthern.edu
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