A characterization of finite unions of interpolation sets in terms of solvability of interpolation problems

She following result is proved: if the restriction of the Hardy class $H\infty$ to a discrete subset $\Lambda$ of the unit disc is exactly the space of all functions on $\Lambda$ that have uniformly bounded divided difference (with respect to hyperbolic metric) of order less than $n$ then $\Lambda$ is a union of $n$ interpolation sets.