  In this article we prove that the $n$-linear operator whose symbol is the
characteristic function of the simplex $\Delta_n = \xi_1 < ... < \xi_n$ is
bounded from $L^2 \times ... \times L^2$ into $L^{2/n}$, generalizing in this
way our previous work on the "bi-est" operator (which corresponds to the case
$n=3$) as well as Lacey-Thiele theorem on the bi-linear Hilbert transform
(which corresponds to the case $n=2$).
