Variational bounds for a dyadic model of the bilinear Hilbert transform
Classical Analysis and ODEs
2012-03-26 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1203.5135,
title = {Variational bounds for a dyadic model of the bilinear Hilbert transform},
author = {Yen Do and Richard Oberlin and Eyvindur Ari Palsson},
journal= {arXiv preprint arXiv:1203.5135},
year = {2012}
}
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14 pages