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arXiv · 1506.00861

Dyadic triangular Hilbert transform of two general and one not too general function

Vjekoslav Kovač·Christoph Thiele·Pavel Zorin-Kranich
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Abstract

The so-called triangular Hilbert transform is an elegant trilinear singular integral form which specializes to many well studied objects of harmonic analysis. We investigate $L^p$ bounds for a dyadic model of this form in the particular case when one of the functions on which it acts is essentially one-dimensional. This special case still implies dyadic analogues of boundedness of the Carleson maximal operator and of the uniform estimates for the one-dimensional bilinear Hilbert transform.

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Vjekoslav Kovač, Christoph Thiele, Pavel Zorin-Kranich. 2015-06-02. Dyadic triangular Hilbert transform of two general and one not too general function. https://doi.org/10.1017/fms.2015.25

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