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

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.

20 pages

Cited by in corpus (10)

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• Singular Brascamp-Lieb inequalities with cubical structure
• Large dilates of hypercube graphs in the plane
• Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity
• The non-resonant bilinear Hilbert--Carleson operator