Weak type inequalities for maximal operators associated to double ergodic sums
نویسندگان
چکیده
Given an approach region Γ ∈ Z+ 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 L(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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