  The Hardy-Rellich inequality given here generalizes a Hardy inequality of
Davies (1984), from the case of the Dirichlet Laplacian of a region
$\Omega\subseteq\real^N$ to that of the higher order polyharmonic operators
with Dirichlet boundary conditions. The inequality yields some immediate
spectral information for the polyharmonic operators and also bounds on the
trace of the associated semigroups and resolvents.
