  In this paper, we introduce regularized trilinear periods on certain
non-reductive groups. It has two direct applications. Firstly, it enables us to
define the regularized Bessel periods and the regularized Fourier-Jacobi
periods for all classical and metaplectic groups. Secondly, by using the
properties of the regularized Fourier-Jacobi periods, we can prove one
direction of the full Gan-Gross-Prasad conjecture on skew-hermitian unitary
groups.
