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Width of the Gakhov class over the Dirichlet space is equal to 2. (English) Zbl 1358.30022
The paper contains a study of the Gakhov class, denoted by \(\mathcal G\). The study of the classical Bloch spaces in [A. V. Kazantsev, in: Geometric theory of functions, boundary value problems and their applications. Proceedings of the international scientific conference, Kazan, Russia, March 2002. Kazan: Kazanskoe Matematicheskoe Obshchestvo. 135–144 (2002; Zbl 1062.30037)] is extended to the classical Dirichlet space \(\mathcal D\). Let \(P:f\longmapsto F=f''/f'\). The main result of the paper is that the radius of the maximal ball in \(P({\mathcal G})\cap {\mathcal D}\) with the center at \(F=0\) is equal to 2.

MSC:
30H30 Bloch spaces
30H99 Spaces and algebras of analytic functions of one complex variable
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