  In this paper, we study Dirichlet problems of fractional Laplace (Poisson)
equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and
Poisson kernels are important tools needed in our study. We first establish the
existence of Green's function by an application of Perron's method. After that,
the Poisson kernel is constructed based on the Green's function. Several
important properties of Green's functions and Poisson kernels are proved.
Finally, we show that the solution of a fractional Laplace (Poisson) equation
under a given condition must be unique and be given by our Green's function and
Poisson kernel.
