Variational bounds for a dyadic model of the bilinear Hilbert transform

@article{Do2012VariationalBF,
  title={Variational bounds for a dyadic model of the bilinear Hilbert transform},
  author={Yen Q. Do and Richard Oberlin and Eyvindur Ari Palsson},
  journal={arXiv: Classical Analysis and ODEs},
  year={2012}
}
We prove variation-norm estimates for the Walsh model of the truncated bilinear Hilbert transform, extending related results of Lacey, Thiele, and Demeter. The proof uses analysis on the Walsh phase plane and two new ingredients: (i) a variational extension of a lemma of Bourgain by Nazarov-Oberlin-Thiele, and (ii) a variation-norm Rademacher-Menshov theorem of Lewko-Lewko. 

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