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Related papers: Bohr inequalities for certain integral operators

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In this paper, we derive the sharp improved versions of Bohr-type inequalities for the Ces\'aro operator acting on the class of bounded analytic functions defined on the unit disk $\D=\left\{z\in\C:\left|z\right|<1\right\}$. In order to…

Complex Variables · Mathematics 2026-04-14 Vasudevarao Allu , Raju Biswas , Rajib Mandal

Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…

Operator Algebras · Mathematics 2007-05-23 Gelu Popescu

In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded…

Functional Analysis · Mathematics 2024-10-28 Vasudevarao Allu , Subhadip Pal

We determine the Bohr radius for the class of odd functions $f$ satisfying $|f(z)|\le 1$ for all $|z|<1$, settling the recent conjecture of Ali, Barnard and Solynin \cite{AliBarSoly}. In fact, we solve this problem in a more general…

Complex Variables · Mathematics 2017-01-17 Ilgiz R Kayumov , Saminathan Ponnusamy

Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, %as applications of these results, we obtain several new…

Complex Variables · Mathematics 2024-09-17 Shanshan Jia , Ming-Sheng Liu , Saminathan Ponnusamy

In this paper, we study the Bohr phenomenon for differential operators $D$ and $\mathscr{D}$ of stable harmonic mappings involving multiple Schwarz functions in $\mathcal{B}_n$, using distance formulations. By constructing suitable…

Complex Variables · Mathematics 2025-11-17 Sujoy Majumder , Nabadwip Sarkar , Molla Basir Ahamed

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…

Complex Variables · Mathematics 2026-04-14 Vasudevarao Allu , Himadri Halder , Subhadip Pal

We prove that the Bohr' radius for large functions is $e^{-\pi }.$

Complex Variables · Mathematics 2020-10-15 Loai Shakaa , Yusuf Abu Muhanna

We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…

Complex Variables · Mathematics 2017-08-21 Ilgiz R Kayumov , Saminathan Ponnusamy

The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on…

Complex Variables · Mathematics 2026-03-18 Vasudevarao Allu , Raju Biswas , Rajib Mandal

Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded…

Complex Variables · Mathematics 2022-05-04 Shankey Kumar

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

Complex Variables · Mathematics 2025-02-06 Wanqing Hou , Qihan Wang , Boyong Long

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…

Complex Variables · Mathematics 2026-03-18 Vasudevarao Allu , Raju Biswas , Rajib Mandal , Hiroshi Yanagihara

In this article, we study the Bohr type inequality for {C}es\'{a}ro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.

Complex Variables · Mathematics 2022-02-15 Vasudevarao Allu , Nirupam Ghosh

This article determines the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the $\ell_p^n$ space and having values in the simply connected domain of…

Complex Variables · Mathematics 2024-09-24 Vibhuti Arora , Shankey Kumar , Saminathan Ponnusamy

This article investigates the Bohr phenomenon and sharp coefficient problems for the class $\mathcal{A}_{\beta}$, a subclass of analytic self-maps of the unit disk with the holomorphic generators of one-parameter continuous semigroups. By…

Complex Variables · Mathematics 2026-04-01 Molla Basir Ahamed , Sanju Mandal

Based on improving the classical Bohr inequality, we get in this paper some refined versions for a quasi-subordination family of functions, one of which is key to build our results. By means of these investigations, for a family of harmonic…

Complex Variables · Mathematics 2021-03-30 Gang Liu , Saminathan Ponnusamy

In this paper, a significant improvement has been achieved in the classical Bohr's inequality for the class $ \mathcal{B} $ of analytic self maps defined on the unit disk $ \mathbb{D} $. More precisely, we generalize and improve several…

Complex Variables · Mathematics 2023-12-27 Molla Basir Ahamed , Sabir Ahammed

In this paper, we study some improved and refined versions of the classical Bohr inequality applicable to the class $\mathcal{B}$, which consists of self-analytic mappings defined on the unit disk $\mathbb{D}$. First, we improve the Bohr…

Complex Variables · Mathematics 2024-02-27 Molla Basir Ahamed , Partha Pratim Roy

We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon…

Functional Analysis · Mathematics 2020-11-26 Bappaditya Bhowmik , Nilanjan Das