Related papers: Functions in Bloch-type spaces and their moduli

Let $u\not\equiv -\infty$ be a subharmonic function on the complex plane $\mathbb C$. Then for any function $r\colon\mathbb C\to (0,1]$ satisfying the condition $$\inf_{z\in\mathbb C}\frac{\ln r(z)}{\ln(2+|z|)}>-\infty,$$ there is an entire…

Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…

We treat the classical concept of domain of holomorphy in $\CC^n$ when the holomorphic functions considered are restricted to lie in some Banach space. Positive and negative results are presented. A new view of the case $n = 1$ is…

We investigate multipliers on the space of holomorphic functions $H(\Omega)$, where $\Omega \subset \mathbb{C}^n$ is an open set. For Runge domains, we characterize these multipliers as convolutions with analytic functionals. Additionally,…

In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $\Omega$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the…

Let $\Omega$ be a complex lattice which does not have complex multiplication and $\wp=\wp_\Omega$ the Weierstrass $\wp$-function associated to it. Let $D\subseteq\mathbb{C}$ be a disc and $I\subseteq\mathbb{R}$ be a bounded closed interval…

Let $C$ be a subset of $\mathbb{R}^n$ (not necessarily convex), $f:C\to\mathbb{R}$ be a function, and $G:C\to\mathbb{R}^n$ be a uniformly continuous function, with modulus of continuity $\omega$. We provide a necessary and sufficient…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

Let $0<\alpha<n$ and $M_{\alpha}$ be the fractional maximal function. The nonlinear commutator of $M_{\alpha}$ and a locally integrable function $b$ is given by $[b,M_{\alpha}](f)=bM_{\alpha}(f)-M_{\alpha}(bf)$. In this paper, we mainly…

We develop a theory of holomorphic functions in several noncommuting (free) variables and thus provide a framework for the study of arbitrary n-tuples of operators. The main topics are the following: Free holomorphic functions and Hausdorff…

Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere…

We study the spectrum $M_b(U)$ of the algebra of bounded type holomorphic functions on a complete Reinhardt domain in a symmetrically regular Banach space $E$ as an analytic manifold over the bidual of the space. In the case that $U$ is the…

Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in \Omega$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(\Omega)$, $1\le p \le…

C-holomorphic functions defined on algebraic sets and having algebraic graphs can be considered as a complex counterpart of regulous functions introduced recently in real geometry. This note is a part of our study on the subject; we prove…

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then f = g up to the multiplication of a unimodular constant, provided the segments make an angle that is an…

Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion…

In this article, we introduce the class $\mathcal{B}^{*}_{\mathcal{H},\Omega}(\alpha)$ of harmonic $\alpha$-Bloch-type mappings on $\Omega$ as a generalization of the class $\mathcal{B}_{\mathcal{H},\Omega}(\alpha)$ of harmonic…

The aim of this paper is two fold. We show that if a complex function $F$ on $\C$ operates in the modulation spaces $M^{p,1}(\R^n)$ by composition, then $F$ is real analytic on $\R^2 \approx \C$. This answers negatively, the open question…

We study functions f(z) holomorphic in the upper half plane and having no zeros when the imaginary part of z is between 0 and 1, and we obtain a lower bound for the modulus of f(z) in this strip. In our analysis we deal with scalar…