Bohr type inequality for certain integral operators and Fourier transform on shifted disks

TL;DR

This paper establishes sharp Bohr type inequalities for certain integral operators and the Fourier transform on a class of bounded analytic functions defined on shifted disks.

Contribution

It extends Bohr inequalities to Cesàro and Bernardi integral operators and the Fourier transform on shifted disks, providing new bounds in complex analysis.

Findings

Derived sharp Bohr inequalities for Cesàro operator

Extended inequalities to Bernardi integral operator and Fourier transform

Applied results to functions on shifted disks

Abstract

In this paper, we derive the sharp Bohr type inequality for the Ces\'aro operator, Bernardi integral operator, and discrete Fourier transform acting on the class of bounded analytic functions defined on shifted disks \beas \Omega_{\gamma}=\left\{z\in\mathbb{C}:\left|z+\frac{\gamma}{1-\gamma}\right|<\frac{1}{1-\gamma}\right\}\quad\text{for}\quad\gamma\in[0,1).\eeas