Dyadic Triangular Hilbert Transform of Two General Functions and One Not Too General Function

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 Lᵖ 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.