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Bohr Inequalities for Certain Classes of Harmonic Mappings

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Abstract

Bohr’s classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. For harmonic mappings of the form \( f=h+\overline{g} \), we obtain an improved version of Bohr inequality for K-quasiregular harmonic mappings in the shifted disk \( \Omega _{\gamma }=\{z\in \mathbb {C}: |z+\frac{\gamma }{1-\gamma }|<\frac{1}{1-\gamma },\; \gamma \in [0,1)\} \) which contains the unit disk \( \mathbb {D} \). In addition, we obtain sharp Bohr inequalities for class of K-quasiconformal harmonic mappings with bounded analytic part.

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Acknowledgements

The authors are greatly indebted to the anonymous referees for their elaborate comments and valuable suggestions, which improve significantly the presentation of the paper. The first author is supported by SERB, SUR/2022/002244, Govt. India and the second author is supported by UGC-JRF (NTA Ref. No.: 201610135853), New Delhi, India.

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  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal,  700032, India

    Molla Basir Ahamed & Sabir Ahammed

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  1. Molla Basir Ahamed
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Ahamed, M.B., Ahammed, S. Bohr Inequalities for Certain Classes of Harmonic Mappings. Mediterr. J. Math. 21, 21 (2024). https://doi.org/10.1007/s00009-023-02564-2

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