Breaking the duality in the return times theorem

By Ciprian Demeter, Michael T. Lacey, Terence Tao, C. Thiele. 2006

53 citations recorded by the source corpus.

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 analog of Bourgain's averages. As an immediate corollary we obtain a Wiener-Wintner type of result for the ergodic Hilbert series.

Subfields: Discrete Mathematics and Combinatorics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1e2d9ba3e324e324da6bac6695da03e956fbeb18

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In Discrete Mathematics and Combinatorics

In Finance

In Statistics and Probability

Citations in the corpus

Discrete maximal functions in higher dimensions and applications to ergodic theory (2014, background): “Although Bourgain’s lemma is interesting in its own right, and is a powerful tool in discrete problems, it has also found wide application in problems susceptible to time-frequency analysis (see e.g. [8, 19, 39]).”
Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020, result): “regime p<1, with the range of exponents being particularly strong in the case of norm convergence on spaces of nite measure. See Section11. A similar \breaking duality" phenomenon occurred in [21]; also, in [53, Theorem 2] a 1This result (and also part (iii)) was claimed in [1]. However, the”