  The twisted paraproduct can be viewed as a two-dimensional trilinear form
which appeared in the work by Demeter and Thiele on the two-dimensional
bilinear Hilbert transform. $L^p$ boundedness of the twisted paraproduct is due
to Kova\v{c}, who in parallel established estimates for the dyadic model of a
closely related quadrilinear form. We prove an $(L^4,L^4,L^4,L^4)$ bound for
the continuous model of the latter by adapting the technique of Kova\v{c} to
the continuous setting. The mentioned forms belong to a larger class of
operators with general modulation invariance. Another instance of such is the
triangular Hilbert transform, which controls issues related to two commuting
transformations in ergodic theory, and for which $L^p$ bounds remain an open
problem.
