Abstract. We study potential theoretic properties of strictly α-stable processes whose Levy measure is comparable to that of a symmetric α-stable process. We show the existence, continuity and strict positivity of transition densities and Green function of the process killed upon exiting a bounded domain. We further show that the exit distributions of the process from a domain satisfying the uniform volume condition have a density. The density is used to establish a representation of regular harmonic functions of the process. Finally, we indicate that the Harnack inequality is true for nonnegative harmonic functions.
2000 Mathematics Subject Classification. 60J35, 60J45, 60J75, 31C99.
Key words and phrases. Nonsymmetric stable processes, transition density, Green function, Poisson kernel, harmonic functions, Harnack inequality.