  In this paper, we study a Dirichlet problem of a fractional Laplace equation
in a bounded Lipschitz domain in $ \R, n \geq 2$. Our main result is that for
the given data $F \in \dot H^s(\Om^c), 0 < s<1$, we find the function which
satisfies that $\De^s u =0$ in $\Om$,
  $u|_{\Om^c} =F$ and $|u|_{\dot{H}^s(\R)} \leq c |F|_{\dot H^s(\Om^c)}$.
Furthermore, we represent the solution with an integral operator.
