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arXiv · 2109.12882

A generalization of the Bohr inequality for bounded analytic functions on simply connected domains and its applications

Shankey Kumar
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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. In this article, we study a generalized Bohr's inequality for the class of bounded analytic functions defined on the simply connected domain $$ \Omega_{\gamma}:=\bigg\{z\in \mathbb{C}: \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}, \,\ \text{for } 0\leq \gamma<1. $$ Part of its applications, we calculate the Bohr-type radii for some known integral operators.

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Shankey Kumar. 2021-09-27. A generalization of the Bohr inequality for bounded analytic functions on simply connected domains and its applications. https://doi.org/10.1080/17476933.2022.2029853

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