Sharpness in Bohr's Inequality

TL;DR

This paper provides a detailed analysis of Bohr's inequality, introducing sharp constants for smaller radii and improving upon previous results by examining the inequality with additional summands.

Contribution

It offers a refined analysis of Bohr's inequality with sharp constants for smaller radii, extending and improving prior results in the field.

Findings

Derived sharp constants for smaller radii in Bohr's inequality

Improved previous bounds and results

Analyzed the impact of additional summands on the inequality

Abstract

We make a careful analysis of Bohr's inequality, in the line started by Kayumov and Ponnusamy, where some extra summand (depending on the function) is added in the right-hand side of the inequality. We analyse the inequality when smaller radius are taken, giving sharp constants. As a result of this point of view, some previous results are improved.