  We characterize the boundedness of Hankel bilinear forms on a product of
generalized Fock-Sobolev spaces on ${\mathbb C}^n$ with respect to the weight
$(1+|z|)^\rho e^{-\frac{\alpha}2|z|^{2\ell}}$, for $\ell\ge 1$, $\alpha>0$ and
$\rho\in{\mathbb R}$. We obtain a weak decomposition of the Bergman kernel with
estimates and a Littlewood-Paley formula, which are key ingredients in the
proof of our main results. As an application, we characterize the boundedness,
compactness and the membership in the Schatten class of small Hankel operators
on these spaces.
