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On the rate of convergence of weighted oscillating ergodic averages

Abstract

Let (X, A, µ) be a probability space, let T be a contraction on L p (µ) and let f in L p (µ), (p > 1). We provide suitable conditions over sequences (w k), (u k) and (A k) in such a way that the weighted ergodic limit lim N →∞ 1 A N N −1 k=0 w k T u k (f) = 0 µ-a.e.. As a consequence of our main theorems, we also deal with the so-called one-sided weighted ergodic Hilbert transforms.
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Dates and versions

hal-03661880 , version 1 (08-05-2022)

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Ahmad Darwiche, Dominique Schneider. On the rate of convergence of weighted oscillating ergodic averages. 2021. ⟨hal-03661880⟩
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