Related papers: Projected composition operators on pseudoconvex do…

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two…

This paper aims to study the boundedness and compactness of composition operators from model spaces to the Hardy Hilbert spaces in the upper half-plane. Consequently, we investigate the boundedness and compactness of composition operators…

In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…

For any real $\beta$ let $H^2_\beta$ be the Hardy-Sobolev space on the unit disc $\mathbb{D}$. $H^2_\beta$ is a reproducing kernel Hilbert space and its reproducing kernel is bounded when $\beta>1/2$. In this paper, we characterize that for…

Let $\phi$ be an analytic self-map and $u$ be a fixed analytic function on the open unit disk $D$ in the complex plane $\CC.$ The weighted composition operator is defined\break by \begin{equation*} uC_\phi f =u \cdot (f\circ \phi), f \in…

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…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

We completely characterize the spectrum of a weighted composition operator $W_{\psi, \varphi}$ on $H^{2}(\mathbb{D})$ when $\varphi$ has Denjoy-Wolff point $a$ with $0<|\varphi '(a)|< 1$, the iterates, $\varphi_{n}$, converge uniformly to…

For a bounded analytic function $\varphi$ on the unit disk $\D$ with $\|\varphi\|_\infty\le1$ we consider the defect operators $D_\varphi$ and $D_{\overline\varphi}$ of the Toeplitz operators $T_\varphi$ and $T_{\overline\varphi}$,…

Let $u$ be a holomorphic function and $\varphi$ a holomorphic self-map of the open unit disk $\mathbb{D}$ in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators $uC_{\varphi}$ from…

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…

Let $\mathbb{B}^d$ be the unit ball on the complex space $\mathbb{C}^d$ with normalized Lebesgue measure $dv.$ For $\alpha\in\mathbb{R},$ denote $k_\alpha(z,w)=\frac{1}{(1-\langle z,w\rangle)^\alpha},$ the Bergman-type integral operator…

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 the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…

Given a symbol $\varphi,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_{\varphi}(f)=f\circ\varphi$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and…

Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb…

We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case…

Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly…

Boundedness of weighted composition operators $W_{u,\varphi}$ acting on the classical Dirichlet space $\mathcal{D}$ as $W_{u,\varphi}f= u\, (f\circ \varphi)$ is studied in terms of the multiplier space associated to the symbol $\varphi$,…

Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…