Open Access
Spring 2013 Variational bounds for a dyadic model of the bilinear Hilbert transform
Yen Do, Richard Oberlin, Eyvindur Ari Palsson
Illinois J. Math. 57(1): 105-119 (Spring 2013). DOI: 10.1215/ijm/1403534488


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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Yen Do. Richard Oberlin. Eyvindur Ari Palsson. "Variational bounds for a dyadic model of the bilinear Hilbert transform." Illinois J. Math. 57 (1) 105 - 119, Spring 2013.


Published: Spring 2013
First available in Project Euclid: 23 June 2014

zbMATH: 1304.42033
MathSciNet: MR3224563
Digital Object Identifier: 10.1215/ijm/1403534488

Primary: 42B20

Rights: Copyright © 2013 University of Illinois at Urbana-Champaign

Vol.57 • No. 1 • Spring 2013
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