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arXiv · 1603.00631

Norm-variation of ergodic averages with respect to two commuting transformations

Polona Durcik·Vjekoslav Kovač·Kristina Ana Škreb·Christoph Thiele
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Abstract

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

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Polona Durcik, Vjekoslav Kovač, Kristina Ana Škreb, Christoph Thiele. 2016-03-02. Norm-variation of ergodic averages with respect to two commuting transformations. https://doi.org/10.1017/etds.2017.48

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