Whitney decomposition, embedding theorems, and interpolation in weighted spaces of analytic functions

According to the classical Whitney theorem, each open set on the plane can be decomposed as a union of special squares whose interiors do not intersect. In the paper, using the properties of Whitney squares, a new concept is introduced. For each center ak of the Whitney square, there is a point a∗k∈C∖G such that the distance to the boundary of the open set G is between two constants, regardless of k. In particular, a necessary and sufficient condition for a sequence (zk)∞1⊂G under which the operator R(f)=(f(z1),f(z2),…,f(zn),…) maps generalized Nevanlinna's flat classes in a domain G of a complex plane in lp.