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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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.

Article information

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

Dates
First available in Project Euclid: 23 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1403534488

Digital Object Identifier
doi:10.1215/ijm/1403534488

Mathematical Reviews number (MathSciNet)
MR3224563

Zentralblatt MATH identifier
1304.42033

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

Citation

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. https://projecteuclid.org/euclid.ijm/1403534488


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References

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