Related papers: Bohr radius for locally univalent harmonic mapping…

In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping $f=h+\overline{g}$, respectively, and also consider the relationship…

In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative $S(f)$ of a locally univalent analytic function $f$ in the unit disk satisfies that $\limsup_{|z|\to 1} |S(f)(z)| (1-|z|^2)^2 < 2$, then there exists a positive…

We compute the exact value of the Bohr radius associated to an elliptic condenser of the complex plane and its Faber polynomial basis.

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…

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family ${\mathcal B}_{H}(\lambda)$ of…

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

Let $\varphi$ be a holomorphic self-map of a bounded homogeneous domain $D$ in $\mathbb{C}^n$. In this work, we show that the composition operator $C_\varphi: f\mapsto f\circ \varphi$ is bounded on the Bloch space $\mathcal{B}$ of the…

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…

Let $\mathcal{H}$ denote the class of all complex-valued harmonic functions $f$ in the open unit disk normalized by $f(0)=0=f_{z}(0)-1=f_{\bar{z}}(0)$, and let $\mathcal{A}$ be the subclass of $\mathcal{H}$ consisting of normalized analytic…

We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older…

In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on…

We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a totally bounded abelian group $(G,w)$ is the Bohr reflection of a locally compact abelian group. Necessary and…

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of…

Let u, v be two harmonic functions in the disk of radius two which have exactly the same set Z of zeros. We observe that the gradient of \log |u/v| is bounded in the unit disk by a constant which depends on Z only. In case Z is empty this…

In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.

We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…

In this paper, we extend the classical Bohr's inequality to the setting of the non-commutative Hardy space $H^1$ associated with a semifinite von Neumann algebra. As a consequence, we obtain Bohr's inequality for operators in the von…

For $r\geq 3$, let $f_r\colon [0,\infty)\to [1,\infty)$ be the unique analytic function such that $f_r({k\choose r})={k-1\choose r-1}$ for any $k\geq r-1$. We prove that the spectral radius of an $r$-uniform hypergraph $H$ with $e$ edges is…

Let $f=h+\overline{g}$ be a harmonic univalent map in the unit disk $\mathbb{D}$, where $h $ and $g$ are analytic. We obtain an improved estimate for the second coefficient of $h$. This indeed is the first qualitative improvement after the…