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JOURNALS // Vestnik KRAUNC. Fiziko-Matematicheskie Nauki // Archive

Vestnik KRAUNC. Fiz.-Mat. Nauki, 2021 Volume 36, Number 3, Pages 40–64 (Mi vkam489)

MATHEMATICS

Integral operators, embedding theorems, Taylor coefficients, isometries, boundary behaviour of area-Nevanlinna type spaces in higher dimension and related problems

R. F. Shamoyan

Department of Mathematics, Bryansk State Technical University

Abstract: This paper contains an overview of recent results of Area-Nevanlinna classes in higher dimension. We here consider various aspects of this new interesting research area of analytic function theory in higher dimension (integral operations, embedding theorems, Taylor coefficients). Previously in one dimension all these results were known. New open interesting Problems in this new research area will be also discussed and indicated.

Keywords: polydisk, unit ball, Taylor coefficients, integral operators, analytic functions, analytic spaces, area Nevanlinna type spaces, tubular domain, pseudoconvex domain, isometries, boundary behaviour.

UDC: 517.55+517.33

MSC: Primary 49J15; Secondary 49N05

Language: English

DOI: 10.26117/2079-6641-2021-36-3-40-64



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