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Breaking the duality in the return times theorem. (English) Zbl 1213.42064
Summary: We prove Bourgain’s return times theorem for a range of exponents $p$ and $q$ that are outside the duality range. An oscillation result is used to prove hitherto unknown almost-everywhere convergence for the signed average analogue of Bourgain’s averages

MSC:
42B25Maximal functions, Littlewood-Paley theory
37A45Relations of ergodic theory with number theory and harmonic analysis
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Full Text: DOI arXiv
References:
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