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Bohr phenomenon for the special family of analytic functions and harmonic mappings. (English) Zbl 1461.30002

Summary: In this paper we obtain the sharp Bohr radius for a family of bounded analytic functions \(\mathcal{B}'\) and for the family of sense-preserving K-quasiconformal harmonic mappings of the form \(f = h + \overline{g}\), where \(h\in \mathcal{B}'\).

MSC:

30A10 Inequalities in the complex plane
30B10 Power series (including lacunary series) in one complex variable
30C62 Quasiconformal mappings in the complex plane
30H05 Spaces of bounded analytic functions of one complex variable
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