  We study the zero exterior problem for the elliptic equation $$
\Delta^{\alpha/2}u-\lambda u=f, \quad x\in D\,; \quad u|_{D^c}=0 $$ as well as
for the parabolic equation $$ u_t=\Delta^{\alpha/2}u+f, \quad t>0,\, x\in D \,;
\quad u(0,\cdot)|_D=u_0, \,u|_{[0,T]\times D^c}=0. $$ Here, $\alpha\in (0,2)$,
$\lambda \geq 0$ and $D$ is a $C^{1,1}$ open set. We prove uniqueness and
existence of solutions in weighted Sobolev spaces, and obtain global Sobolev
and H\"older estimates of solutions and their arbitrary order derivatives. We
measure the Sobolev and H\"older regularities of solutions and their arbitrary
derivatives using a system of weights consisting of appropriate powers of the
distance to the boundary. The range of admissible powers of the distance to the
boundary is sharp.
