Open AccessMultiple interpolation in the Privalov classes in a disk
Author(s) -
Eugenia G. Rodikova
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2101271r
Subject(s) - mathematics , interpolation (computer graphics) , unit disk , class (philosophy) , function (biology) , analytic function , combinatorics , discrete mathematics , pure mathematics , image (mathematics) , computer science , artificial intelligence , evolutionary biology , biology
For all 0 < q < +? the Privalov class ?q consists of all analytic functions f in a unit disk such that sup 0?r<1 1/2? ??,-? (ln+ |f(rei?)|)q d?< +?. In this paper we solve a multiple interpolation problem in the class ?q for all 0 < q < 1. Namely, we find the sufficient conditions for the explicit construction of the function that solves the interpolation problem in the Privalov class. In addition, we discuss the necessity of these conditions.