Related papers: Schatten class Hankel and $\overline{\partial}$-Ne…

We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p < \infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's theorem holds under the hypothesis that…

Using several complex variables techniques, we investigate the interplay between the geometry of the boundary and compactness of Hankel operators. Let f be a function smooth up to the boundary on a smooth bounded pseudoconvex domain D in…

We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $\Omega \subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For…

Let $d\geq1$, $\Omega$ be a bounded domain of a smooth complete Riemannian d-manifold M, and $\mu$ be a positive finite Borel measure with compact support in $\overline{\Omega}$. We prove the Courant nodal domain theorem for the…

Let $L$ be a second order elliptic operator $L$ with smooth coefficients defined on a domain $\Omega $ in $\mathbb{R}^d $, $d\geq3$, such that $L1\leq 0$. We study existence and properties of continuous solutions to the following problem…

We prove some characterizations of Schatten class Toeplitz operators on Bergman spaces of tube domains over symmetric cones for small exponents.

Let $\varphi $ be a negative plurisubharmonic function in a pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ and $f$ be a bounded holomorphic function belonging to $L^{2}(\Omega, \varphi)$. For all negative plurisubharmonic functions $\psi$…

Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Forn\ae ss index of $\Omega$ is $1$,…

We characterize the membership of Hankel operators with general symbols in the Schatten Classes $S^p,\, p\in(0,1),$ of the large Bergman spaces $A^2_{\omega}$. The case $p\geq 1$ was proved by Lin and Rochberg.

In this paper, we characterize the essential norm of Hankel operators from a weighted Fock space $F_{\varphi}^{p}$ to a weighted Lebesgue space $L_{\varphi}^{q}$ for all $1 \leq p, q < \infty$. Additionally, we characterize the Schatten-$h$…

Let $\mathcal{H}$ be a separable Hilbert space and let $A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with exponential weights. In the present paper, we give the complete characterizations for the boundedness and…

The d-bar-Neumann operator on (0,q)-forms ($1\le q \le n$) on a bounded convex domain Omega in C^n is compact if and only if the boundary of Omega contains no complex analytic (equivalently: affine) variety of dimension greater than or…

We consider a bounded open subset $\Omega$ of ${\mathbb{R}}^n$ of class $C^{1,\alpha}$ for some $\alpha\in]0,1[$ and the space $V^{-1,\alpha}(\partial\Omega)$ of (distributional) normal derivatives on the boundary of $\alpha$-H\"{o}lder…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

We consider the zeta function $\zeta\_\Omega$ for the Dirichlet-to-Neumann operator of a simply connected planar domain $\Omega$ bounded by a smooth closed curve.We prove non-negativeness and growth properties for…

Let $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every} frame $\{f_n\}$ in $H$; and for $0<p\le2$,…

On a bounded smooth pseudoconvex domain in $\mathbb{C}^n$ with $n >2$, inspired by the compactness condition introduced by Yue Zhang, we present the new sufficient condition for the exact regularity of the $\overline\partial$-Neumann…

A well known result of C. Cowen states that, for a symbol $\varphi \in L^{\infty }, \; \varphi \equiv \bar{f}+g \;\;(f,g\in H^{2})$, the Toeplitz operator $T_{\varphi }$ acting on the Hardy space of the unit circle is hyponormal if and only…

We study the holomorphic Hardy-Orlicz spaces H^\Phi(\Omega), where \Omega is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function \Phi is in particular such that H…

We consider the zeta function $\zeta_\Omega$ for the Dirichlet-to-Neumann operator of a simply connected planar domain $\Omega$ bounded by a smooth closed curve of perimeter $2\pi$. We prove that $\zeta_\Omega''(0)\ge…