Variational bounds for a dyadic model of the bilinear Hilbert transform

Details Variational bounds for a dyadic model of the bilinear Hilbert transform Variational bounds for a dyadic model of the bilinear Hilbert transform

2012-03-22

arxiv.org/abs/1203.5135v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

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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