We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calderón–Zygmund operators as several functions can now depend on the same one-dimensional variable. The study of this class is motivated by examples related to the two-dimensional bilinear Hilbert transform and to bilinear ergodic averages. This paper is a sequel to a prior paper by the first author.
"A T(1) theorem for entangled multilinear dyadic Calderón–Zygmund operators." Illinois J. Math. 57 (3) 775 - 799, Fall 2013. https://doi.org/10.1215/ijm/1415023510