The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space

TL;DR

This paper extends Bohr inequalities to lacunary and alternating series for holomorphic functions in finite-dimensional Banach spaces, including vector-valued cases and higher dimensions.

Contribution

It introduces new Bohr inequalities for lacunary and alternating series in finite-dimensional Banach spaces, including vector-valued functions and higher-dimensional extensions.

Findings

Established Bohr inequalities for lacunary series in Banach spaces

Extended Bohr inequalities to vector-valued holomorphic functions

Generalized inequalities to higher-dimensional spaces

Abstract

In this paper, we study the Bohr inequality with lacunary series to the single valued (resp. vector-valued) holomorphic function defined in unit ball of finite dimensional Banach sequence space. Also, we extend the Bohr inequality with an alternating series to the higher-dimensional space.