  It is shown that the second term in the asymptotic expansion as $t\to 0$ of
the trace of the semigroup of symmetric stable processes (fractional powers of
the Laplacian) of order $\alpha$, for any $0<\alpha<2$, in Lipschitz domains is
given by the surface area of the boundary of the domain. This brings the
asymptotics for the trace of stable processes in domains of Euclidean space on
par with those of Brownian motion (the Laplacian), as far as boundary
smoothness is concerned.
