Mathematics & Physics 2016, 9(1), 69-78 УДК 517.53 On Interpolation in the Class of Analytic Functions in the Unit Disk with the Nevanlinna Characteristic from Lp-spaces Eugenia G.Rodikova∗ Bryansk State University Bezhitskaya, 14, Bryansk, 241036 Russia Received 02.11.2015, received in revised form 08.12.2015, accepted 12.01.2016 In this paper we solve the interpolation problem for the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces under the condition that interpolation nodes are contained in a finite union of Stolz angles. <...> Note that Sp ∫ π −π { f ∈ H(D) : ∫ 1 0 (1−r)αTp(r, f)dr < +∞ , α as (see [14]): } ln+ |f(reiϕ)|dϕ is the Nevanlinna characteristic of the function f, this paper we investigate the questions of interpolation in Sp α. α-classes are a natural generalization of the Nevanlinna-Djrbashian classes. <...> In solving the problem of free interpolation, that is, with minimal restrictions imposed on the interpolated function, it is important to find a natural class to which the restriction of on the interpolation set to belong. <...> Eugenia G.Rodikova On Interpolation in the Class of Analytic Functions in the Unit Disk . <...> In this article we answer the question under what conditions on the sequence {αk}+∞k=1 the operator R(f) maps the class Sp α onto the class lp α. <...> A sequence {αk}+∞k=1 is called interpolating for Sp α if R(Sp α) = lp α. <...> Let us note that the solution of interpolation problems in the various classes of analytic functions has been widely discussed by Russian and foreign scientists: A.GNaftalevic [7], H. Shapiro and A. Shields [11], S. A. Vinogradov, V.P.Havin [16], M.Djrbashian [4], N. A. Shirokov and A.M.Kotochigov [6], K. Seip [12], A.Hartmann [5], V.A. Bednazh and F. A.Shamoyan [1] and etc. <...> The fundamental result in this area belongs to the L. Carleson [2]. <...> The paper is organized as follows: in the first section we present the formulation of main result of the article and give some auxiliary results, in the second section we present the proof of main result. 1. <...> Formulation of main result and proof of auxiliary results To formulate and proof the results of the work we introduce some more notation <...>