Estimates of Green function for relativistic α-stable process

We call an R-d-valued stochastic process X-t with characteristic function exp {-t{(m(2/alpha)+|xi|(2))(alpha/2) - m}},xi is an element of R-d,m > 0, the relativistic alpha-stable process. In the paper we derive sharp estimates for the Green function of the relativistic alpha-stable process on C-1,C-1 domains. Using these estimates we provide lower and upper bounds for the Poisson kernel. As another application we derive 3G Theorem and Boundary Harnack Principle for C-1,C-1 domains.