Related papers: Compact Hankel Operators with Bounded Symbols
This paper presents a comprehensive study of H-Toeplitz operators on the Fock space, a class of operators that synthesizes structural elements of both Toeplitz and Hankel operators. We derive explicit matrix representations for these…
We prove sufficient conditions for the boundedness and compactness of Toeplitz operators $T_a$ in weighted sup-normed Banach spaces $H_v^\infty$ of holomorphic functions defined on the open unit disc $\mathbb{D}$ of the complex plane; both…
In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from…
We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on ${\mathbb C}^n$ with respect to the weight $(1+|z|)^\rho e^{-\frac{\alpha}2|z|^{2\ell}}$, for $\ell\ge 1$, $\alpha>0$ and…
We consider bounded Hankel operators $H_{\psi}$ acting on the Hardy space $H^2$ to $L^2\ominus H^2$ and obtain results on the Schmidt subspaces $E^+_s(H_\psi)$ of such operators defined as the kernels of $ H_{\psi}^{\ast}H_{\psi}-s^2I$…
For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…
We introduce and systematically study a class of operators that arise naturally due to the Beurling decomposition of the Hardy space $H^2=K_\theta \oplus \theta H^2$. While the compressions of classical Toeplitz and Hankel operators to the…
In this paper, we study the behavior of the singular values of Hankel operators on weighted Bergman spaces $A^2_{\omega _\varphi}$, where $\omega _\varphi= e^{-\varphi}$ and $\varphi$ is a subharmonic function. We consider compact Hankel…
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…
The boundedness of the small Hankel operator $h^\omega_{f}(g)=\overline{P_\omega}(fg)$ induced by a measurable symbol $f$ and the Bergman projection $P_\omega$ associated to a radial weight $\omega$ acting from the weighted Bergman space…
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…
We prove the spectral mapping theorem $\sigma_e(A_\phi) = \phi(\sigma_e(A_z))$ for the Fredholm spectrum of a truncated Toeplitz operator $A_\phi$ with symbol $\phi$ in the Sarason algebra $C+H^\infty$ acting on a coinvariant subspace…
We study Toeplitz operators on the Bargmann space, whose Toeplitz symbols are exponentials of complex inhomogeneous quadratic polynomials. Extending a result by Coburn--Hitrik--Sj\"{o}strand, we show that the boundedness of such Toeplitz…
We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness…
Let $\D=\D_1\setminus \Dc_2$, where $\D_1$ and $\D_2$ are two smooth bounded pseudoconvex domains in $\C^n, n\geq 3,$ such that $\Dc_2\subset \D_1.$ Assume that the $\dbar$-Neumann operator of $\D_1$ is compact and the interior of the…
We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The…
In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal H(b)$, where the symbol $b$ is a rational function in the unit ball of $H^\infty$ that is…
We establish a connection between compactness of Hankel operators and geometry of the underlying domain through compactness multipliers for the $\overline{\partial}$-Neumann operator. In particular, we prove that any compactness multiplier…
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…
We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{\Phi_1} (\mathbb B^n)$ into $H^{\Phi_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?\Phi_1$…