Pointwise convergence of the ergodic bilinear Hilbert transform

2006/01/12 by Ciprian Demeter, Demeter, Ciprian · 1 citation
Mathematics · #37A05 #42B20 #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.math/0601277

openalex publication_date 2006/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bf X=(X, Σ, m, τ) be a dynamical system. We prove that the bilinear series \sideset'∑_n=-N^N\fracf(τⁿx)g(τ^-nx)n converges almost everywhere for each f,g∈ L^∞(X). We also give a proof along the same lines of Bourgain's analog result for averages.

Cited by

• More stability and convergence results for higher-order Wiener-Wintner systems

Related

• On the two dimensional Bilinear Hilbert Transform
• Pointwise ergodic theorems for non-conventional bilinear averages along (\lfloor n^c\rfloor,-\lfloor n^c\rfloor)
• On the homogeneous ergodic bilinear averages with M "obius and\n liouville weights
• Strictly ergodic models and the convergence of non-conventional pointwise ergodic averages
• Pointwise convergence of multiple ergodic averages and strictly ergodic models