Pointwise convergence of certain continuous-time double ergodic averages

Joris Roos; Michael Christ; Polona Durcik; Vjekoslav Kova\v{c}

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Pointwise convergence of certain continuous-time double ergodic averages

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arxiv 2011.06370 v2 pith:NDLLMVY2 submitted 2020-11-12 math.DS math.CA

Pointwise convergence of certain continuous-time double ergodic averages

Michael Christ , Polona Durcik , Vjekoslav Kova\v{c} , Joris Roos This is my paper

classification math.DS math.CA

keywords averagescontinuous-timeconvergencemathbbactionactionscertaincomes

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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.

Pointwise convergence of certain continuous-time double ergodic averages

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