Related papers: On the Berger-Coburn phenomenon

Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is…

We discuss the compactness of Hankel operators on Hardy, Bergman and Fock spaces with focus on the differences between the three cases, and complete the theory of compact Hankel operators with bounded symbols on the latter two spaces with…

The authors provide a correct proof of Theorem 1.2 and correct the statement of Theorem 2.6 in their paper, which appeared in Trans. Amer. Math. Soc. 375 (2022), 3733-3753.

We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on ${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where $\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the corresponding Bergman…

Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on $\cn$. The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that…

In this paper, for $1 \leq p, r < \infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F^p_\alpha$ to $L^p_\alpha$. The main result shows that the $r$-summing norm of $H_f$…

In this paper, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are $C^3$-logarithmic growth functions with mild smoothness conditions. It is shown that a Hankel…

We study small Hankel operators $h_b$ with operator-valued holomorphic symbol $b$ on a class of vector-valued Fock type spaces. We show that the boundedness / compactness of $h_b$ is equivalent to the membership of $b$ to a specific growth…

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 $\mathcal{H}$ 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…

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.

We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors…

In this paper, we use the non-increasing rearrangement of ${\rm IDA}$ function with respect to a suitable measure to characterize the asymptotic behavior of the singular values sequence $\{s_n(H_f)\}_n$ of Hankel operators $H_f$ acting on a…

We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, and use it to completely characterize boundedness and compactness of Hankel operators on weighted Fock spaces. As an…

In this paper, we study operator-theoretic properties (boundedness and compactness) of Hankel operators on the Fock-sobolev spaces $ \mathscr{F}^{p,m} $ in terms of $ \mathcal{BMO}_r^p $ and $ \mathcal{VMO}_r^p $ spaces, respectively, for a…

We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<\infty$ of the Hankel operators $H_ f$ and $H_{\bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function,…

We show that for $f$ a continuous function on the closed polydisc $\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition $f=h+g$, where $h$…

We study big Hankel operators acting on vector-valued Fock spaces with radial weights in $\C^d$. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.

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…

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 $0<p\le2$,…