Breaking the duality in the return times theorem

Details Breaking the duality in the return times theorem Breaking the duality in the return times theorem

2006-01-18

arxiv.org/abs/math/0601455v2

Mathematics

Dynamical Systems

62 pages, 0 figures. Minor changes. This is the final version of the paper. To appear in Duke Math J

Scientific paper

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.

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