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Pointwise convergence of certain continuous-time double ergodic averages
Published online by Cambridge University Press: 04 May 2021
Abstract
We prove almost everywhere 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.
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- © The Author(s), 2021. Published by Cambridge University Press
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