Related papers: On Shapiro's Compactness Criterion for Composition…

We consider Ces\'aro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit…

In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables formula. With the same formula, we characterise the bounded…

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted…

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 study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of…

Let $\phi$ be a linear-fractional self map of the open unit disk, not an automorphism, such that $\phi(\zeta)=\eta$ for distinct points $\zeta,\eta$ in the unit circle. We consider the question of which composition operators lie in the…

We study the C$^*$ algebra generated by the composition operator $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circ\varphi_a$, where $$ \varphi_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. Also several operators…

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…

Let $\phi(z)=(\phi_1(z), ...,\phi_n(z))$ be a holomorphic self-map of $U^n$ and $\psi(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and…

We characterize the (essentially) decreasing sequences of positive numbers $\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) are bounded, where H 2 ($\beta$) is the space of analytic functions f in the unit disk…

In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we…

In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of…

We continue the work of \cite{TLNT}. Let $E$ be a non-Blaschke subset of the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$. Fixed $1\leq p\leq \infty$, let $H^p(\mathbb{D})$ be the Hardy space of holomorphic functions in the disk…

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…

In this paper, we study the complex symmetry of weighted composition-differentiation operator $D_{n, \psi, \phi}$ on weighted Bergman spaces $\mathcal{A}^2_{\alpha}$ with respect to the conjugation $C_{\mu, \eta}$ for $\mu, \eta \in \{z\in…

We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences $\beta$ every symbol $\varphi \colon \mathbb{D} \to \mathbb{D}$ with $\varphi \in H^2 (\beta)$ induces a bounded composition…

We characterize those non-negative, measurable functions $\psi$ on $[0,1]$ and positive, continuous functions $\omega_1$ and $\omega_2$ on $\mathbb R^+$ for which the generalized Hardy-Ces\`aro operator $$(U_{\psi}f)(x)=\int_0^1…

In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator $W_{\phi,\psi}$ to be bounded and compact are…

We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal…

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…