Pointwise convergence of certain continuous-time double ergodic averages

Abstract

We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving ${\mathbb{R}}^2$-action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.

9 pages, v2 incorporates a minor fix/simplification in the proof

References in corpus (2)

• Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
• On Trilinear Oscillatory Integral Inequalities and Related Topics