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In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition…
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…
While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$,…
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 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 paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of…
In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…
In this paper, we study the boundedness and the compactness of the little Hankel operators $h_b$ with operator-valued symbols $b$ between different weighted vector-valued Bergman spaces on the open unit ball $\mathbb{B}_n$ in…
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…
We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…
We provide an estimate for the essential norm of a weighted composition operator $W_{\psi,\varphi}\colon f\mapsto \psi(f\circ\varphi)$ acting on the space $BMOA$ in terms of the weight function $\psi$ and the $n$-th power $\varphi^n$ of the…
We show that the weighted Bergman-Orlicz space $A\_{\alpha}^{\psi}$ coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function $\psi$ satisfies the so-called $\Delta^{2}$--condition. In addition we…
We found several new equivalent characterizations for the boundedness and compactness of the differences of weighted differentiation composition operators from Bloch-type space to weighted-type space. Especially, we estimated its essential…
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
Let $\mathbb{D}$ denote the unit disk of $\mathbb{C}$ and let $\Lambda^\alpha(\mathbb{D})$ denote the scale of holomorphic Lipschitz spaces extended to all $\alpha\in\mathbb{R}$. For arbitrary $\alpha, \beta\in\mathbb{R}$, we characterize…
In this paper, we obtain the essential norm estimate for the difference of two weighted composition operators acting on standard weighted Bergman spaces over the unit ball. And we get some characterizations for the difference of weighted…
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…