Higher order derivative characterization for Fock-type spaces
type: Item
instance of: scholarly article
title: Higher order derivative characterization for Fock-type spaces
zbMATH Open document ID: 1338.30051
author: Sei-Ichiro Ueki
published in: Integral Equations and Operator Theory
publication date: 2016-01-26T00:00:00Z
review text: For \(\alpha>0\) and \(n\in\mathbb{N}\), the Fock-type space \(\mathcal{F}_\alpha^\infty(\mathbb{C}^n)\) consists of those entire functions \(f\) on \(\mathbb{C}^n\) for which \[ \|f\|_{\infty, \alpha} =\sup_{z\in\mathbb{C}^n} |f(z)|\exp\left(-\frac{\alpha}{2} |z|^2 \right) < \infty. \] The author characterizes \(\mathcal{F}_\alpha^\infty(\mathbb{C}^n)\) in terms of higher-order derivatives of \(f\). As an application, he studies the boundedness and compactness of the extended Cesàro operator on \(\mathcal{F}_\alpha^\infty(\mathbb{C}^n)\) and \(\mathcal{F}_{\alpha, 0}^\infty(\mathbb{C}^n)\).
reviewed by: Evgueni Doubtsov
Mathematics Subject Classification ID: 30H20
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 6535955
zbMATH Keywords: Fock spaces
zbMATH Keywords: extended Cesaro operators
MaRDI profile type: Publication
full work available at URL: s00020-015-2246-1
OpenAlex ID: W753179719
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DOI: 10.1007/S00020-015-2246-1
description: scientific article; zbMATH DE number 6535955