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On the Ergodic Averages and the Ergodic Hilbert Transform

Canadian Journal of Mathematics, 1995
AbstractLet T be an invertible measure-preserving transformation on a σ-finite measure space (X, μ) and let 1 < p < ∞. This paper uses an abstract method developed by José Luis Rubio de Francia which allows us to give a unified approach to the problems of characterizing the positive measurable functions v such that the limit of the ergodic ...
Fernández-Cabrera, L. M.   +2 more
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Differential and ergodic transforms

Mathematische Annalen, 2002
Let \(\tau\) be an ergodic transformation with respect to a non-atomic measure. Operators of the form \[ T_nf(x)=\sum_{k=1}^nv_k\left((1/n_k)\sum_{j=0}^{n_k-1}f(\tau^jx)- (1/n_{k-1})\sum_{j=0}^{n_{k-1}-1}f(\tau^jx)\right) \] for a lacunary sequence \((n_k)\) and \(\ell^{\infty}\) sequence of weights \((v_k)\) are shown to converge a.e. and in \(L^p\), \
Jones, Roger L., Rosenblatt, Joseph
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