Convergence and divergence of averages along subsequences in certain Orlicz spaces

2009/01/07 by Christopher M. Wedrychowicz, Wedrychowicz, C. M.
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.0901.0932

openalex publication_date 2009/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical theorem of Birkhoff states that the T^N f(x) = (1/N)∑_k=0^N-1 f(σ^k x) converges almost everywhere for x∈ X and f∈ L¹(X), where σ is a measure preserving transformation of a probability measure space X. It was shown that there are operators of the form T^N f(x)=(1/N)∑_k=0^N-1f(σ^n_kx) for a subsequence \n_k\ of the positive integers that converge in some L^p spaces while diverging in others. The topic of this talk will examine this phenomenon in the class of Orlicz spaces \LLog^βL:β>0\.

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