  We study uniform Sobolev inequalities for the second order differential
operators $P(D)$ of non-elliptic type. For $d\ge3$ we prove that the Sobolev
type estimate $\|u\|_{L^q(\mathbb{R}^d)}\le C \|P(D)u\|_{L^p(\mathbb{R}^d)}$
holds with $C$ independent of the first order and the constant terms of $P(D)$
if and only if $1/p-1/q=2/d$ and $\frac{2d(d-1)}{d^2+2d-4}<p<\frac{2(d-1)}d$.
We also obtain restricted weak type endpoint estimates for the critical
$(p,q)=(\frac{2(d-1)}{d},\frac{2d(d-1)}{(d-2)^2})$, $(\frac{2d(d-1)}{d^2+2d-4},
\frac{2(d-1)}{d-2})$. As a consequence, the result extends the class of
functions for which the unique continuation for the inequality $|P(D)u|\le|Vu|$
holds.
