Interpolating sequences in mean (Q1782269)

The author considers interpolation problems in the space of bounded analytic functions in the disk as well as in spaces of analytic Hölder functions. Given a target sequence $\{w_n\}_{n\ge1}$ and a sequence of points $\{z_n\}_{n\ge1}$ in the unit disc, the author searches for functions $f$ in the given class that satisfy the equalities \[ \frac{f(z_1)+\cdots+f(z_n)}{n}=w_n,\quad n\ge1. \] He describes target spaces when the corresponding interpolating sequences are uniformly separated or the union of two uniformly separated sequences.