Pointwise convergence of the ergodic bilinear Hilbert transform

Ciprian Demeter

Let $\mathbf{X}=(X,\Sigma ,m,\tau )$ 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 $…