English
Related papers

Related papers: Hankel operators on the Fock-Sobolev spaces

200 papers

We study big Hankel operators $H_f^\nu:A^p_\omega \to L^q_\nu$ generated by radial Bekoll\'e-Bonami weights $\nu$, when $1<p\leq q<\infty$. Here the radial weight $\omega$ is assumed to satisfy a two-sided doubling condition, and…

Complex Variables · Mathematics 2018-06-27 José Ángel Peláez , Antti Perälä , Jouni Rättyä

We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin…

Functional Analysis · Mathematics 2014-11-05 Inyoung Park

In this paper, we investigate the boundedness of Toeplitz product $T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ on Fock-Sobolev space for two polynomials $f$ and $g$ in $z,\overline{z}\in\mathbb{C}^{n}$. As a result, the boundedness of…

Functional Analysis · Mathematics 2021-07-30 Yiyuan Zhang , Guangfu Cao , Li He

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…

Complex Variables · Mathematics 2021-03-08 Zeljko Cuckovic , Sonmez Sahutoglu

This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…

Functional Analysis · Mathematics 2025-07-10 Oinam Nilbir Singh , M. P. Singh , Thokchom Sonamani Singh

In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…

Functional Analysis · Mathematics 2025-07-21 Cezhong Tong , Zicong Yang , Zehua Zhou

For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to…

Analysis of PDEs · Mathematics 2013-11-05 Chokri Abdelkefi , Mongi Rachdi

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\geq 0}$ with entries…

Complex Variables · Mathematics 2022-07-25 Shanli Ye , Zhihui Zhou

In this article, we investigate the (big) Hankel operators $H_f$ on Hardy spaces of strongly pseudoconvex domains with smooth boundaries in $\mathbb{C}^n$. We also give a necessary and sufficient condition for boundedness of the Hankel…

Complex Variables · Mathematics 2021-02-09 Bo-Yong Chen , Liangying Jiang

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 $?\Phi_1$…

Classical Analysis and ODEs · Mathematics 2012-06-01 Benoit F. Sehba , Edgar Tchoundja

If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…

Complex Variables · Mathematics 2018-05-23 Daniel Girela , Noel Merchán

In this paper, we extend the Brown-Halmos theorems to the Fock space and investigate the range of the Berezin transform. We observe that there are non-pluriharmonic functions $u$ that can be written as a finite sum…

Complex Variables · Mathematics 2023-09-26 Jie Qin

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on…

Functional Analysis · Mathematics 2021-04-26 Tom Carroll , Clifford Gilmore

We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers,…

Functional Analysis · Mathematics 2015-08-05 Fawwaz Batayneh , Mishko Mitkovski

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class…

Functional Analysis · Mathematics 2009-07-15 Eva A. Gallardo-Gutiérrez , Romesh Kumar , Jonathan R. Partington

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…

Classical Analysis and ODEs · Mathematics 2026-03-19 Denis Zelent

We study the compactness of composition operators on the Bergman spaces of certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained in the boundary. As a consequence we characterize that compactness of the…

Complex Variables · Mathematics 2022-04-18 Timothy G. Clos

We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…

Complex Variables · Mathematics 2017-04-13 Pham Trong Tien , Le Hai Khoi

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

Operator Algebras · Mathematics 2018-02-06 Andreas Andersson

We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral…

Functional Analysis · Mathematics 2024-06-03 Wolfram Bauer , Robert Fulsche , Miguel Angel Rodriguez Rodriguez