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Pointwise convergence of the ergodic bilinear Hilbert transform

Ciprian Demeter
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Abstract

Let ${\bf X}=(X, Σ, m, τ)$ be a dynamical system. We prove that the bilinear series $\sideset{}{'}\sum_{n=-N}^{N}\frac{f(τ^nx)g(τ^{-n}x)}{n}$ 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.

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Ciprian Demeter. 2006-01-12. Pointwise convergence of the ergodic bilinear Hilbert transform. https://arxiv.org/abs/math/0601277

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