Breaking the duality in the return times theorem
Dynamical Systems
2012-05-08 v2 Classical Analysis and ODEs
Abstract
We prove Bourgain's Return Times Theorem for a range of exponents and 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.
Cite
@article{arxiv.math/0601455,
title = {Breaking the duality in the return times theorem},
author = {Ciprian Demeter and Michael Lacey and Terence Tao and Christoph Thiele},
journal= {arXiv preprint arXiv:math/0601455},
year = {2012}
}
Comments
62 pages, 0 figures. Minor changes. This is the final version of the paper. To appear in Duke Math J