Free Interpolation in the Spaces of Analytic Functions With Derivative of Order s From the Hardy Space

Abstract

We consider the problem of free interpolation for the spaces of analytic functions with derivative of order s in the Hardy space Hp. For the sets that satisfy the Stolz condition, we obtain a condition necessary for interpolation: if 1 ≤ p < ∞, then the set must be a union of s sparse sets. For p = ∞, we obtain a necessary and sufficient condition for interpolation: the set must be a union of s + 1 sparse sets. In this case, we construct an extension operator. Bibliography 11 titles.