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Width of the Gakhov class over the Dirichlet space is equal to 2

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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.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Department of Mathematical Statistics, Kazan (Volga Region) Federal University, Kremlevskaya ul. 35, Kazan, 420008, Tatarstan, Russia

    A. V. Kazantsev

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  1. A. V. Kazantsev
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Correspondence to A. V. Kazantsev.

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Submitted by Alexandr Elizarov

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Kazantsev, A.V. Width of the Gakhov class over the Dirichlet space is equal to 2. Lobachevskii J Math 37, 449–454 (2016). https://doi.org/10.1134/S1995080216040120

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  • DOI: https://doi.org/10.1134/S1995080216040120

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