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May 2016 Compact Weighted Composition Operators Between Generalized Fock Spaces
Waleed Al-Rawashdeh
Missouri J. Math. Sci. 28(1): 62-75 (May 2016). DOI: 10.35834/mjms/1474295356


Let $\psi$ be an entire self-map of the $n$-dimensional Euclidean complex space $\mathbb{C}^n$ and $u$ be an entire function on $\mathbb{C}^n$. A weighted composition operator induced by $\psi$ with weight $u$ is given by $(uC_{\psi}f)(z)= u(z)f(\psi(z))$, for $z \in \mathbb{C}^n$ and $f$ is the entire function on $\mathbb{C}^n$. In this paper, we study weighted composition operators acting between generalized Fock-types spaces. We characterize the boundedness and compactness of these operators act between $\mathcal{F}_{\phi}^{p}(\mathbb{C}^n)$ and $\mathcal{F}_{\phi}^{q}(\mathbb{C}^n)$ for $0\lt p, q\leq\infty$. Moreover, we give estimates for the Fock-norm of $uC_{\psi}: \mathcal{F}_{\phi}^{p}\rightarrow \mathcal{F}_{\phi}^{q}$ when $0\lt p, q\lt \infty$, and also when $p=\infty$ and $0\lt q\lt \infty$.


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Waleed Al-Rawashdeh. "Compact Weighted Composition Operators Between Generalized Fock Spaces." Missouri J. Math. Sci. 28 (1) 62 - 75, May 2016.


Published: May 2016
First available in Project Euclid: 19 September 2016

zbMATH: 1362.47005
MathSciNet: MR3549808
Digital Object Identifier: 10.35834/mjms/1474295356

Primary: 47B38
Secondary: 30C40 , 30D15 , 30D20 , 44A15 , 44A20

Keywords: ‎Berezin transform , bounded operators , Carleson measures , ‎compact‎ ‎operators , entire functions , generalized Fock spaces , weighted composition operators

Rights: Copyright © 2016 Central Missouri State University, Department of Mathematics and Computer Science


Vol.28 • No. 1 • May 2016
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