Interpolation sequences in area Privalov classes in disk

Abstract

In the work we obtain a necessary and sufficient condition for the zeros of analytic functions in area Privalov classes $\tilde{\Pi}_q$ $(0<q<1)$ in the unit circle $D=\{z\in \mathbb{C}: |z|<1\}$ located in the Stolz angles. We solve the free interpolation problem in these classes under the condition that the interpolation nodes are located in the Stolz angles. We also solve the interpolation problem in the area Privalov classes in circle on Carleson sets.