We consider the α-stable Ornstein–Uhlenbeck process in {mathbb{R}}^d with the generator TeXL = Delta^{alpha/2} - lambda x cdotnabla_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 does not hold
