Related papers: Bohr phenomenon for certain classes of harmonic ma…

In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…

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

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $\mathcal{B}$, which consists of analytic self-mappings defined on the unit disk $\mathbb{D}$. We improve the Bohr-Rogosinski…

This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…

This article focuses on the Bohr radius problem for the derivatives of analytic functions, along with a technique of establishing Bohr inequalities in classical and generalized settings.

Let $f$ be a complex-valued harmonic mapping defined in the unit disk $\mathbb D$. We introduce the following notion: we say that $f$ is a Bloch-type function if its Jacobian satisfies $$ \sup_{z\in\mathbb D}(1-|z|^2)\sqrt{|J_f(z)|}<\infty.…

If $f$ is a nonzero Bohr almost periodic function on $\mathbb R$ with a bounded spectrum we prove there exist $C_f > 0$ and integer $n > 0$ such that for every $u > 0$ the mean measure of the set $\{\, x \, : \, |f(x)| < u \, \}$ is less…

In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the…

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…

Denote by $\Omega(n)$ the number of prime divisors of $n \in \mathbb{N}$ (counted with multiplicities). For $x\in \mathbb{N}$ define the Dirichlet-Bohr radius $L(x)$ to be the best $r>0$ such that for every finite Dirichlet polynomial…

We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum of two analytic functions: the first is unbounded and…

We prove that if $(\varphi_n)_{n=0}^\infty, \; \varphi_0 \equiv 1, $ is a basis in the space of entire functions of $d$ complex variables, $d\geq 1,$ then for every compact $K\subset \mathbb{C}^d$ there is a compact $K_1 \supset K$ such…

This article introduces the notion of arithmetic Bohr radius for operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using tools from local Banach space theory, we determine its asymptotic behavior in…

In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic…

In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr…

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…

H\"{o}lder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and it is, without any doubt, one of the milestones in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and…

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…