Illinois Journal of Mathematics

Variational bounds for a dyadic model of the bilinear Hilbert transform

Yen Do, Richard Oberlin, and Eyvindur Ari Palsson

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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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Illinois J. Math., Volume 57, Number 1 (2013), 105-119.

First available in Project Euclid: 23 June 2014

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Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)


Do, Yen; Oberlin, Richard; Palsson, Eyvindur Ari. Variational bounds for a dyadic model of the bilinear Hilbert transform. Illinois J. Math. 57 (2013), no. 1, 105--119. doi:10.1215/ijm/1403534488.

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