相关论文: Composition Operators on $\bf H^{p,q,s}(B_{n})$ of…

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…

Suppose $n\geq 3$ and let $B$ be the open unit ball in $\mathbb{R}^n$. Let $\varphi: B\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $\psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition…

Let $n\ge 1$ and $\varphi: \mathbb{D}^n\to\mathbb{D}$ be a holomorphic function, where $\mathbb{D}$ denotes the open unit disk of $\mathbb{C}$. Let $\Theta: \mathbb{D} \to \mathbb{D}$ be an inner function and $K^p_\Theta$, $p>0$, denote the…

Let $\psi$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $\varphi$ be a holomorphic self-map of $\BB$, associated with normal weights $\nu$ and $\mu$. We consider the weighted composition operator $…

Let $\varphi$ be a linear fractional self-map of the open unit disk $\mathbb{D}$ and $H^2$ the Hardy space of analytic functions on $\mathbb{D}$. The goal of this article is to characterize the linear fractional composition operators…

Let $\phi$ be an analytic map taking the unit disk $\mathbb{D}$ into itself. We establish that the class of composition operators $f \mapsto C_\phi(f) = f \circ \phi$ exhibits a rather strong rigidity of non-compact behaviour on the Hardy…

Let $\varphi_j$, $j=1,2, \dots, N$, be holomorphic self-maps of the unit disk $\mathbb{D}$ of $\mathbb{C}$. We prove that the compactness of a linear combination of the composition operators $C_{\varphi_j}: f\mapsto f\circ\varphi_j$ on the…

Suppose $\mathcal{H}$ is a weighted Hardy space of analytic functions on the unit ball $\mathbb{B}_n\subset\mathbb{C}^n$ such that the composition operator $C_\psi$ defined by $C_{\psi}f=f\circ\psi$ is bounded on $\mathcal{H}$ whenever…

We consider the invariant subspace of composition operators on Hardy space $H^p$ where the composition operators corresponding to a function $\varphi$ that is a holomorphic self-map of $\mathbb D$. Firstly, we discuss composition operators…

Let $\phi(z)=(\phi_1(z),...,\phi_n(z))$ be a holomorphic self-map of $B_n$ and $\psi(z)$ a holomorphic function on $B_n$, and $H(B_n)$ the class of all holomorphic functions on $B_n$, where $B_n$ is the unit ball of $C^n$, the weight…

Let $\varphi$ be a holomorphic map which is a symbol of a bounded composition operator $C_\varphi$ acting on the Hardy-Hilbert space of Dirichlet series. We find a K\"onigs map for $\varphi$. We then deduce several applications on…

V. Matache (J. Operator Theory 73(1):243--264, 2015) raised an open problem about characterizing composition operators $C_{\phi}$ on the Hardy space $H^2$ and nonzero singular measures $\mu_1$, $\mu_2$ on the unit circle such that…

In this paper we show that a composition operator $C_\varphi$ cannot be complex symmetric on Hardy-Hilbert space $H^2(D)$ when $\varphi$ is an elliptic automorphism of order $3$ and not a rotation. This completes the project of finding all…

When $\varphi$ and $\psi$ are linear-fractional self-maps of the unit ball $B_N$ in ${\mathbb C}^N$, $N\geq 1$, we show that the difference $C_{\varphi}-C_{\psi}$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any…

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $\varphi(s)=c_0s+\varphi_0(s)$, where $\varphi_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic…

In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions…

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…

Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic…

We give a necessary and sufficient condition for a holomorphic self-map $\phi$ of the tridisc to induce a bounded composition operator on the associated Hardy space. This condition depends on the behaviour of the first and the second…

Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…