Related papers: Integration operators on Hardy and Bergman spaces
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…
We define a scale of Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, $p\in[1,\infty]$, that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for $p=1$. We also introduce a notion of…
In this article, we introduce a new class of conjugations in the scalar valued Hardy space $H^2_{\mathbb{C}}(\mathbb{D})$ and provide a characterization of a complex symmetric Toeplitz operator $T_{\phi}$ with respect to these newly…
In this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}C_{1}T$, where $T$ is an unitary operator and $C_{1}f\left(z\right)=\overline{f\left(\overline{z}\right)}$, with $f\in H^{2}$. In the…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
In this work, we establish results on the continuity of strongly singular Calder\'on-Zygmund operators of type $\sigma$ on Hardy spaces $H^p(\mathbb{R}^n)$ for $0<p\leq 1$ assuming a weaker $L^{s}-$type H\"ormander condition on the kernel.…
Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…
We study concentration operators acting on the Fourier symmetric Sobolev space $H$ consisting of functions $f$ such that $\int_{\mathbb{R}} |f(x)|^2(1+x^2) dx + \int_{\mathbb{R}} |\hat{f}(\xi)|^2(1+\xi^2) d\xi < \infty $. We find that the…
In this paper, some characterizations for the compact difference of composition operators on Bergman spaces $A^p_\omega$ with doubling weight are given, which extend Moorhouse's characterization for the difference of composition operators…
In thius paper we introduce the Hardy and Bergman spaces on hyperconvex domains relative to a acontinuous exhaustion function. We prove their basic properties and study their composition operators induced by holomorphic mappings between…
Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the…
In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with a rapidly decreasing weight $\omega=e^{-\eta}$, $\Delta\eta>0$. In addition, we provide simple…
In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two…
In this paper, for $1\leq p<\infty$, we provide several descriptions of Schatten $p$-class Hankel operators $H_f$ and $H_{\overline{f}}$ on the weight Bergman space $A^2_\omega$, in terms of a certain global and local mean oscillation of…
Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operator and the Hodge-Kodaira Laplacian acting on functions has…
The paper gives the background for Toeplitz $T_a$ and Hankel $H_a$ operators acting between distinct Hardy type spaces over the unit circle $\mathbb{T}$. We characterize possible symbols of such operators and prove general versions of…
Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…
We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on various subclasses of analytic functions in the unit disk.…
This paper aims to study the boundedness and compactness of composition operators from model spaces to the Hardy Hilbert spaces in the upper half-plane. Consequently, we investigate the boundedness and compactness of composition operators…