Harnack inequalities for Ornstein-Uhlenbeck processes driven by Lévy processes

By using the existing sharp estimates of the density function for rotationally invariant symmetric [alpha]-stable Lévy processes and rotationally invariant symmetric truncated [alpha]-stable Lévy processes, we obtain that the Harnack inequalities hold for rotationally invariant symmetric [alpha]-stable Lévy processes with [alpha][set membership, variant](0,2) and Ornstein-Uhlenbeck processes driven by rotationally invariant symmetric [alpha]-stable Lévy process, while the logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated [alpha]-stable Lévy processes.