Related papers: Generalized Hilbert Operator Acting on Hardy Space…

A Hankel operator $\Gamma$ in $L^2(\mathbb{R}_+)$ is an integral operator with the integral kernel of the form $h(t+s)$, where $h$ is known as the kernel function. It is known that $\Gamma$ is positive semi-definite if and only if $h$ is…

For $p>p_0=\frac{2\lambda}{2\lambda+1}$ with $\lambda>0$, the Hardy space $H_{\lambda}^p(\mathbb{R}_+^2)$ associated with the Dunkl transform $\mathcal{F}_\lambda$ and the Dunkl operator $D$ on the real line $\mathbb{R}$, where…

In this paper we introduce a more general class of Foguel-Hankel operators, where the unilateral shift on $\ell^2(\mathbb{N}) $ is replaced by a general multiplication operator on the Hardy space $H^2$ . We prove that Peller's condition is…

We characterize the positive Borel measures such that the differentiation operator of order $n\in\mathbb{N}\cup\{0\}$ is compact from the Hardy space $H^p$ into $L^q(\mu)$, $0<p,q<\infty$.

We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space…

Generalized Toeplitz plus Hankel operators $T(a)+H_{\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\alpha$ changing the orientation of the unit circle $\mathbb{T}$ are considered on the Hardy spaces…

In this paper, we study Hausdorff operator $\mathcal{H}_\mu$ on a large class of weighted mixed norm Fock spaces $F_\phi^{p,q}$ for $1\leq p,q\leq\infty$. The boundedness and compactness of $\mathcal{H}_\mu$ on $F_\phi^{p,q}$ are…

We study $L^p(\mu)$ estimates for the commutator $[H,b]$, where the operator $H$ is a dyadic model of the classical Hilbert transform introduced in \cite{arXiv:2012.10201,arXiv:2212.00090} and is adapted to a non-doubling Borel measure…

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which…

Let $\mu$ be a finite positive Borel measure on the interval $[0, 1)$ and $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n} \in H(\mathbb{D})$. The Ces\`aro-like operator is defined by $$ \mathcal {C}_{\mu}…

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…

For $0<p<\infty $, the Dirichlet-type space $\Dp$ consists of those analytic functions $f$ in the unit disc $\D$ such that $\int_\D|f'(z)|\sp p(1-|z|)^{p-1}\,dA(z)<\infty$. Motivated by operator theoretic differences between the Hardy space…

In this note, we introduce and study a new kind of generalized Ces\`aro operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for which…

Suppose $\alpha>-1$ and $1\leq p \leq \infty$. Let $f=P_{\alpha}[F]$ be an $\alpha$-harmonic mapping on $\mathbb{D}$ with the boundary $F$ being absolute continuous and $\dot{F}\in L^p(0,2\pi)$, where…

In this paper, we calculate the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ from the logarithmically weighted Korenblum space $H^\infty_{\alpha,\log}$ into Korenblum space $H^\infty_\alpha$, and from the Hardy space…

In this paper, we study necessary and sufficient conditions for a positive Borel measure $\mu$ on the complex space $\mathbb{C}$ to be a $(\infty,q)$ or $(p,\infty)$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we…

Let $L$ be a one to one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the Hardy space…

Let $\theta$ be an inner function satisfying the connected level set condition of B. Cohn, and let $K^{1}_{\theta}$ be the shift-coinvariant subspace of the Hardy space $H^1$ generated by $\theta$. We describe the dual space to…

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…

We consider the weighted Bergman spaces HL^2(B^d,\mu_{\lambda}), where d\mu_\lambda(z)=c_{\lambda}(1-|z|^2)^lambda d\tau, \tau being the hyperbolic volume measure. These spaces are nonzero if and only if \lambda>d. For 0<\lambda\leq d,…