Related papers: Generalized Volterra operators mapping between Ban…

Let $H(\mathbb{D})$ be the space of all analytic functions in the unit disc $\mathbb{D}$. For $g\in H(\mathbb{D})$, the generalized Hilbert operator $\mathcal{H}_{g}$ is defined by $$\mathcal{H}_{g}(f)(z)=\int_{0}^{1}f(t)g'(tz)dt, \ \ z\in…

A classical result of Calkin [Ann. of Math. (2) 42 (1941), pp. 839-873] says that an inner derivation $S\mapsto [T,S] = TS-ST$ maps the algebra of bounded operators on a Hilbert space into the ideal of compact operators if and only if $T$…

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

We obtain a necessary and sufficient condition for the operator of integration to be bounded on $H^\infty$ in a simply connected domain. The main ingredient of the proof is a new result on uniform approximation of Bloch functions. This…

For a Dirichlet series g, we study the Volterra operator Tg of symbol g, acting on a class of weighted Hilbert spaces of Dirichlet series. We obtain sufficient / necessary conditions for Tg to be bounded (resp. compact), involving BMO and…

Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of…

An investigation is made of the generalized Ces\`aro operators $C_t$, for $t\in [0,1]$, when they act on the space $H(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$, on the Banach space $H^\infty$ of bounded…

We completely describe the boundedness of the Volterra type operator $J_ g$ between Hardy spaces in the unit ball of $\Cn$. The proof of the one dimensional case used tools, such as the strong factorization for Hardy spaces, that are not…

Let $n$ be a positive integer and $\mathbf{g}=(g_0,g_1,\cdots,g_{n-1})$, with $g_k\in H(\mathbb{D})$ for $k=0,1,\cdots,n-1$. Let $I_{\mathbf{g}}^{(n)}$ be the generalized Volterra-type operators on $H(\mathbb{C})$, which is represented as…

In this paper, we investigate the boundedness and compactness of generalized integration operators $T_g^{n,k}$ and $S_g^{n,0}$ from analytic tent spaces $AT_p^\infty(\alpha)$ to $AT_q^\infty(\beta)$ when $0<p,q<\infty,\alpha,\beta>-2$.

Let $f$ and $g$ be analytic on the unit disc $\mathbb{D}$. The integral operator $T_g$ is defined by $ T_g f(z) = \int_0^z f(t)g'(t)\,dt$, $z \in \mathbb{D}$. The problem considered is characterizing those symbols $g$ for which $T_g$ acting…

On the space of bounded analytic functions and the Bloch space on the unit disk, we study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators. Further, we consider the…

For analytic functions $g$ on the unit disc with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator $T_g(f)(z)=\int_0^zf(\zeta)g'(\zeta)\,d\zeta$ from a space $X$ of analytic functions…

For g in BMOA, we consider the generalized Volterra operator T_g acting on Hardy spaces H^p. This article aims to study the largest space of analytic functions, which is mapped by T_g into the Hardy space H^p. We call this space the optimal…

~In this paper, we investigate the boundedness of some Volterra-type operators between ~$Zygmund$~ type spaces. Then, we give the essential norms of such operators in terms of ~$g,\varphi$, their derivatives and the n-th power ~$\varphi^n$…

The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…

For an almost radial and typical weight $v$, we characterize the continuity and compactness of the weighted composition operator $u C_{\varphi}$ acting on the weighted Banach spaces of analytic functions $H_{v}^{\infty}$ in terms of the…

We study the boundedness of Toeplitz operators $T_\psi$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $\mathbb{R}^n$. Generalizing earlier results for analytic function spaces, we derive a general…

We prove that a Volterra-type integral operator $T_gf(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta, \, z \in \mathbb D,$ defined on Hardy spaces $H^p, \, 1 \le p < \infty,$ fixes an isomorphic copy of $\ell^p,$ if the operator $T_g$ is not…

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded…