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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