Related papers: Composition operators from logarithmic Bloch space…

Let $\varphi$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_{\varphi}$ is compact on the Bergman space if and only if $\varphi(\overline{\mathbb{D}^2})\cap…

Let $\mathbb{D}$ be the open unit disk in $\mathbb{C}$, let $H^2$ denote the Hardy space on $\mathbb{D}$ and let $\varphi : \mathbb{D} \rightarrow \mathbb{D}$ be a holomorphic self map of $\mathbb{D}$. The composition operator $C_{\varphi}$…

We consider composition operators $\mathscr{C}_\varphi$ on the Hardy space of Dirichlet series $\mathscr{H}^2$, generated by Dirichlet series symbols $\varphi$. We prove two different subordination principles for such operators. One…

The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic…

By a theorem of Bayart, $\varphi$ generates a bounded composition operator on the Hardy space $\Hp$of Dirichlet series ($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is a nonnegative integer and $\psi$ a Dirichlet series…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is…

Given pointed metric spaces $X$ and $Y$, we characterize the basepoint-preserving Lipschitz maps $\phi$ from $Y$ to $X$ inducing an isometric composition operator $C_\phi$ between the Lipschitz spaces $Lip_0(X)$ and $Lip_0(Y)$, whenever $X$…

We characterize the weighted composition-differentiation operators $D_{\mfn,\psi,\varphi}$ acting on $\mathcal{H}_\gamma(\mathbb{D}^d)$ over the polydisk $\mathbb{D}^d$ which are complex symmetric with respect to the conjugation…

Let $ \mathcal{H}(\mathbb{D}) $ be the class of all holomorphic functions in the unit disk $ \mathbb{D} $. We aim to explore the complex symmetry exhibited by generalized weighted composition-differentiation operators, denoted as $L_{n,…

Let $\varphi:\mathbb{D} \to \mathbb{D}$ be a holomorphic map with a fixed point $\alpha\in\mathbb{D}$ such that $0\leq |\varphi'(\alpha)|<1$. We show that the spectrum of the composition operator $C_\varphi$ on the Fr\'echet space $…

We study the strong continuity of weighted composition semigroups of the form $T_tf=\varphi_t'\left(f\circ\varphi_t\right)$ in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that…

In this article, we completely characterize the positive expansive and absolutely Ces\`aro composition operators $C_{\phi}f=f\circ \phi$ induced by affine self-maps $\phi$ of the right half-plane $\mathbb{C}_+$ on the weighted Bergman space…

In this paper, we study the boundedness and compactness of the differences of two weighted composition operators acting from $\alpha$-Bloch space to $\beta$-Bloch space on the open unit disk. This study has a relationship to the topological…

In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…

We construct an analytic self-map $\phi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\phi$ is compact on the Hardy-Orlicz space $H^\Psi$, but not compact on the Bergman-Orlicz space…

Let $\zeta$ and $\eta$ be distinct points on the unit circle and suppose that $\phi$ is a linear-fractional self-map of the unit disk D, not an automorphism, with $\phi(\zeta)=\eta$. We describe the C*-algebra generated by the associated…

Let $\phi$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_{\phi}f=f\circ \phi$ on the Hardy space $H^2(\mathbb{D}).$ We mainly characterize all…

We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness…

Let $\varphi: B_d\to\mathbb{D}$, $d\ge 1$, be a holomorphic function, where $B_d$ denotes the open unit ball of $\mathbb{C}^d$ and $\mathbb{D}= B_1$. Let $\Theta: \mathbb{D} \to \mathbb{D}$ be an inner function and let $K^p_\Theta$ denote…