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Ufa Mathematical Journal, 2021, Volume 13, Issue 4, Pages 80–90
DOI: https://doi.org/10.13108/2021-13-4-80
(Mi ufa593)
 

This article is cited in 1 scientific paper (total in 1 paper)

On coefficient multipliers for area Privalov classes

E. G. Rodikova

Bryansk State University, Bezhitskaya str. 14, 241050, Bryansk, Russia
References:
Abstract: The problem of describing the Taylor coefficients of functions analytic in a disk was first resolved for the Nevanlinna class by an outstanding Soviet mathematician S.N. Mergelyan in the beginning of 20th century. Later, the studies devoted to obtaining similar estimates in various classes of analytic functions were made by known Russian and foreign specialists in the complex analysis: G. Hardy, J. Littlewood, A.A. Friedman, N. Yanagihara, M. Stoll, S.V. Shvedenko and others.
In the paper we introduce a area Privalov class $\tilde{\Pi}_q$, $(q>0)$, being a generalization of a known area Nevanlinna class. In the first part of the paper we obtain a sharp estimate for the growth of an arbitrary function in the area Privalov class, we describe the Taylor coefficients for this function. In the second part of the work, on the base of the obtained estimates we describe completely the coefficient multipliers from area Privalov classes into the Hardy classes. In a simplified form this problem can be formulated as follows: by what factors the Taylor coefficients of a function in a given class $\tilde{\Pi}_q$, $q>0$, should be multiplied in order to get the Taylor coefficients of a function in a Hardy class.
Keywords: area Privalov class, Taylor coefficients, multiplier, growth, analytic functions.
Received: 31.01.2021
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30H50; Secondary 30H10, 30H15
Language: English
Original paper language: Russian
Citation: E. G. Rodikova, “On coefficient multipliers for area Privalov classes”, Ufa Math. J., 13:4 (2021), 80–90
Citation in format AMSBIB
\Bibitem{Rod21}
\by E.~G.~Rodikova
\paper On coefficient multipliers for area Privalov classes
\jour Ufa Math. J.
\yr 2021
\vol 13
\issue 4
\pages 80--90
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\crossref{https://doi.org/10.13108/2021-13-4-80}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124306832}
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  • https://doi.org/10.13108/2021-13-4-80
  • https://www.mathnet.ru/eng/ufa/v13/i4/p82
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:119
    Russian version PDF:69
    English version PDF:14
    References:17
     
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