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

Vasudevarao Allu, Raju Biswas, Rajib Mandal, Hiroshi Yanagihara

Abstract

In this paper, we investigate several Bohr radii associated with the Cesáro operator, Bernardi integral operator, $β$-Cesáro 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 $\mathbb{C}^n$.

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

Abstract

In this paper, we investigate several Bohr radii associated with the Cesáro operator, Bernardi integral operator, -Cesáro 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 within the space .
Paper Structure (2 sections, 5 theorems, 99 equations, 1 figure)

This paper contains 2 sections, 5 theorems, 99 equations, 1 figure.

Table of Contents

  1. Introduction and Preliminaries
  2. Main results

Key Result

Lemma 2.1

DP2008 If $f(z)=\sum_{n=0}^\infty a_n z^n$ is holomorphic in $\mathbb{D}$ with $|f(z)|\leq1$ in $\mathbb{D}$, then we have

Figures (1)

  • Figure 1: The graph of $G_1(r)$ in (0, 1)

Theorems & Definitions (9)

  • Lemma 2.1
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof