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

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