V. N. Dubinin, “Bounded holomorphic functions in a circular annulus”, Algebra i Analiz, 36:6 (2024), 30

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Algebra i Analiz, 2024, Volume 36, Issue 6, Pages 30–46 (Mi aa1945)

Research Papers

Bounded holomorphic functions in a circular annulus

V. N. Dubinin

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

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Abstract: Using the symmetrization method, new covering and distortion theorems are proved for holomorphic and bounded functions in a circular annulus that preserve one of its boundary components. In particular, inequalities including the Schwarzian derivative at a boundary point of the annulus are established. As corollaries, we consider differential inequalities for functions that are weakly univalent in the disk. Unsolved problems are given.

Keywords: holomorphic functions, covering theorems, distortion theorems, Schwarzian derivative, condenser capacity, symmetrization.

Funding agency	Grant number
Ministry of Science and Higher Education of the Russian Federation	075-00459-24-00

Received: 10.05.2024

Document Type: Article

Language: Russian

Citation: V. N. Dubinin, “Bounded holomorphic functions in a circular annulus”, Algebra i Analiz, 36:6 (2024), 30–46

Citation in format AMSBIB

\Bibitem{Dub24}

\by V.~N.~Dubinin

\paper Bounded holomorphic functions in a circular annulus

\jour Algebra i Analiz

\yr 2024

\vol 36

\issue 6

\pages 30--46

\mathnet{http://mi.mathnet.ru/aa1945}

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https://www.mathnet.ru/eng/aa1945

https://www.mathnet.ru/eng/aa/v36/i6/p30

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	134
Full-text PDF :	4
References:	20
First page:	24

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