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

@article{Durcik2017NormVO, title={Norm variation of ergodic averages with respect to two commuting transformations}, author={Polona Durcik and Vjekoslav Kova{\vc} and Kristina Ana {\vS}kreb and Christoph Thiele}, journal={Ergodic Theory and Dynamical Systems}, year={2017}, volume={39}, pages={658 - 688} }

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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