Pointwise convergence of the ergodic bilinear Hilbert transform

Ciprian Demeter

Pointwise convergence of the ergodic bilinear Hilbert transform

Classical Analysis and ODEs 2007-05-23 v1 Dynamical Systems

Authors: Ciprian Demeter

Abstract

Let ${\bf X}=(X, \Sigma, m, \tau)$ be a dynamical system. We prove that the bilinear series $\sideset{}{'}\sum_{n=-N}^{N}\frac{f(\tau^nx)g(\tau^{-n}x)}{n}$ converges almost everywhere for each $f,g\in L^{\infty}(X).$ We also give a proof along the same lines of Bourgain's analog result for averages.

Cite

@article{arxiv.math/0601277,
  title  = {Pointwise convergence of the ergodic bilinear Hilbert transform},
  author = {Ciprian Demeter},
  journal= {arXiv preprint arXiv:math/0601277},
  year   = {2007}
}

Comments

28 pages, no figures

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