Email this article Width of the Gakhov class over the Dirichlet space is equal to 2
- Authors: Kazantsev A.V.1
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Affiliations:
- Institute of Computational Mathematics and Information Technologies, Department of Mathematical Statistics
- Issue: Vol 37, No 4 (2016)
- Pages: 449-454
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198078
- DOI: https://doi.org/10.1134/S1995080216040120
- ID: 198078
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Abstract
Gakhov class G is formed by the holomorphic and locally univalent functions in the unit disk with no more than unique critical point of the conformal radius. Let D be the classical Dirichlet space, and let P: f ↦ F = f″/f′. We prove that the radius of the maximal ball in P(G)∩D with the center at F = 0 is equal to 2.
About the authors
A. V. Kazantsev
Institute of Computational Mathematics and Information Technologies, Department of Mathematical Statistics
Author for correspondence.
Email: kazandrey0363@rambler.ru
Russian Federation, Kremlevskaya ul. 35, Kazan, Tatarstan, 420008
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