On the Bohr inequality with a fixed zero coefficient
Complex Variables
2019-04-01 v1
Abstract
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination 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.
Keywords
Cite
@article{arxiv.1903.12646,
title = {On the Bohr inequality with a fixed zero coefficient},
author = {Seraj A. Alkhaleefah and Ilgiz R Kayumov and Saminathan Ponnusamy},
journal= {arXiv preprint arXiv:1903.12646},
year = {2019}
}
Comments
12 pages; The article has been accepted to appear in Proceedings of the American Mathematical Soceity