On Harnack inequality for \(\alpha\)-stable Ornstein-Uhlenbeck processes (Q2471029)

Consider the \(\alpha \)-stable Ornstein-Uhlenbeck process in \(\mathbb{R}^{d}\) with generator \(L=\Delta ^{\alpha /2}-\lambda x\cdot \nabla_{x}\). The author shows that if \(1\leq \alpha <2\) or \(\alpha <1=d\), then the Harnack inequality holds. A counterexample is constructed for \(\alpha <1<d\) to show that the Harnack inequality does not hold in this case.