On Harnack inequality for α-stable Ornstein-Uhlenbeck processes

We consider the α-stable Ornstein-Uhlenbeck process in Rd with the generator L = ∆α/2 − λx · ∇x. We show that if 2> α ≥ 1 or α < 1 = d the Harnack inequality holds. For α < 1 < d we construct a counterexample that shows that the Harnack inequality doesn’t hold