On the Bohr inequality with a fixed zero coefficient

Alkhaleefah, Seraj; Kayumov, Ilgiz; Ponnusamy, Saminathan

doi:10.1090/proc/14634

On the Bohr inequality with a fixed zero coefficient

Authors: Seraj A. Alkhaleefah, Ilgiz R. Kayumov and Saminathan Ponnusamy
Journal: Proc. Amer. Math. Soc. 147 (2019), 5263-5274
MSC (2010): Primary 30A10, 30B10, 30C62, 30H05, 31A05, 41A58; Secondary 30C75, 40A30
DOI: https://doi.org/10.1090/proc/14634
Published electronically: July 30, 2019
MathSciNet review: 4021086
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Abstract: In this paper, we introduce the study of the Bohr phenomenon for a quasisubordination family of functions, and establish the classical Bohr's inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain the exact version of the classical Bohr's inequality for bounded analytic functions and also for -quasiconformal harmonic mappings by replacing the constant term by the absolute value of the analytic part of the given function. We also obtain the Bohr radius for the subordination family of odd analytic functions.

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