Related papers: Generalized Hilbert Operators

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\beta > 0$, The generalized Hankel matrix $\mathcal{H}_{\mu,\beta}= (\mu_{n,k,\beta})_{n,k\geq0}$ with entries $\mu_{n,k,\beta}=…

Let g be an analytic function on the open unit disc U such that g(U) is contained in U, and let h be an analytic function on U such that the weighted composition operator W_{h,g) defined by W_{h,g}f = h f(g) is bounded on the Hardy space…

We consider the Hilbert-type operator defined by $$ H_{\omega}(f)(z)=\int_0^1 f(t)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the…

In this article we address the question of characterizing the sequences of complex numbers $(\eta )=\{ \eta_n\}_{n=0}^\infty $ whose associated Rhaly operator $\mathcal R_{(\eta )}$ is bounded or compact on the Hardy spaces $H^p$ ($1\le…

In this paper, the boundedness and compactness of generalized integration operators $T_g^{n,k}$ between different analytic tent spaces in the unit disc are completely characterized.

Let $\alpha>0$ and $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\ge0}$ with entries…

It is well known that the Hilbert matrix operator $\mathcal {H}$ is bounded from $H^{\infty}$ to the mean Lipschitz spaces $\Lambda^{p}_{\frac{1}{p}}$ for all $1<p<\infty$. In this paper, we prove that the range of Hilbert matrix operator…

In the present work, we are interested in compact integration operators $I_g f(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta$ acting on the Hardy space $H^2$ and on the weighted Bergman spaces $\mathcal{A}^2_\alpha$. We give upper and lower…

In this article we consider the generalized integral operators acting on the Hilbert space $H^2$. We characterize when these operators are uniform, strong and weakly asymptotic Toeplitz and Hankel operators. Moreover we completely describe…

Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\alpha>0$, the generalized Hankel matrix $\mathcal{H}_{\mu, \alpha}=(\mu_{n, k, \alpha})_{n, k \geq 0}$ with entries $\mu_{n, k, \alpha}=\int_{[0,1)}…

We introduce a natural generalization of a well studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give…

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 characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces

In this article, we characterize the radial operators on weighted Bergman spaces of Reinhardt domains in $\mathbb{C}^n$, the Dirichlet and the Hardy spaces of the open unit disk $\mathbb{D}$, in terms of integral representations. We also…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

This note completely describes the bounded or compact Riemann-Stieltjes integral operators $T_g$ acting between the weighted Bergman space pairs $(A^p_\alpha,A^q_\beta)$ in terms of particular regularities of the holomorphic symbols $g$ on…

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$. We obtain a collection of general…

If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…