Related papers: Essential norm of composition operators Harmonic B…
We obtain a description of the homeomorphisms which induce bounded composition operators on Sobolev spaces of functions on metric measure spaces.
The kernel of composition operator $C_T$ on Orlicz-Sobolev space is obtained. Using the kernel, a necessary and a sufficient condition for injectivity of composition operator $C_T$ has been established. Composition operators on…
In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting…
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…
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…
We propose a survey on composition operators in classical Sobolev spaces. We mention results obtained in 2019, on the continuity of such operators.
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…
Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on…
In this paper the necessary and sufficient conditions for the product of composition operators to be isometry are obtained on weighted Bergman space. With the help of a counter example we also proved that unlike on…
In this article, we completely characterize the Berezin range of Toeplitz operators with harmonic symbols acting on weighted Bergman spaces, illustrating the necessity of the harmonicity condition through examples. We then introduce a new…
In this paper we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.
Let $\varphi$ be a holomorphic self-map of a bounded homogeneous domain $D$ in $\mathbb{C}^n$. In this work, we show that the composition operator $C_\varphi: f\mapsto f\circ \varphi$ is bounded on the Bloch space $\mathcal{B}$ of the…
The aim of this paper is to give the answer to the problem of characterization of acting conditions (necessary as well as sufficient) for composition operators in some sequence spaces. We also characterize their boundedness and local…
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 thesis we study three problems. The first is the superposition of the operators and their proprities, such as boundedness,continuity,regularity and the inequalities of the norms of the composition of functions in some functional…
In this paper, we study the basic properties such as boundedness and compactness of composition operators on discrete analogue of generalized Hardy space defined on a homogeneous rooted tree. Also, we compute the operator norm of…
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…
We introduce two kinds of operator-valued norms. One of them is an $L(H)$-valued norm. The other one is an $L(C(K))$-valued norm. We characterize the completeness with respect to a bounded $L(H)$-valued norm. Furthermore, for a given Banach…
We define positive Toeplitz operators between weighted harmonic Bloch spaces $b^\infty_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full range of parameter $\alpha\in\mathbb{R}$. We give characterizations of bounded and compact…
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'{e}chet space of the entire mappings that are bounded on bounded sets the composition turns to be…