Bohr phenomenon for certain integral operators and transforms in complex Banach spaces

TL;DR

This paper explores Bohr radii related to various integral operators and transforms acting on holomorphic functions in complex Banach spaces, extending classical Bohr phenomena to new operator contexts.

Contribution

It introduces new Bohr radii estimates for operators like Cesàro, Bernardi, and Fourier transforms in complex Banach spaces, broadening the scope of Bohr phenomena.

Findings

Derived bounds for Bohr radii of Cesàro and Bernardi operators

Established Bohr radius estimates for the discrete Fourier transform

Extended Bohr phenomenon to holomorphic mappings in Banach spaces

Abstract

In this paper, we investigate several Bohr radii associated with the Ces\'aro operator, Bernardi integral operator, $\beta$-Ces\'aro operator, and discrete Fourier transform, all defined on a set of holomorphic mappings from the unit ball of a complex Banach space into the closure of the unit polydisc $\mathbb{D}^n$ within the space $\mathbb{C}^n$.