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May 2014 Composition Operators on Generalized Weighted Nevanlinna Class
Waleed Al-Rawashdeh
Missouri J. Math. Sci. 26(1): 14-22 (May 2014). DOI: 10.35834/mjms/1404997105


Let $\varphi$ be an analytic self-map of open unit disk $\mathbb{D}$. The operator given by $(C_{\varphi}f)(z)=f(\varphi(z))$, for $z \in \mathbb{D}$ and $f$ analytic on $\mathbb{D}$ is called a composition operator. Let $\omega$ be a weight function such that $\omega\in L^{1}(\mathbb{D}, dA)$. The space we consider is a generalized weighted Nevanlinna class $\mathcal{N}_{\omega}$, which consists of all analytic functions $f$ on $\mathbb{D}$ such that $\displaystyle \|f\|_{\omega}=\int_{\mathbb{D}}\log^{+}(|f(z)|) \omega(z) dA(z)$ is finite; that is, $\mathcal{N}_{\omega}$ is the space of all analytic functions belong to $L_{\log^+}(\mathbb{D}, \omega dA)$. In this paper we investigate, in terms of function-theoretic, composition operators on the space $\mathcal{N}_{\omega}$. We give sufficient conditions for the boundedness and compactness of these composition operators.


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Waleed Al-Rawashdeh. "Composition Operators on Generalized Weighted Nevanlinna Class." Missouri J. Math. Sci. 26 (1) 14 - 22, May 2014.


Published: May 2014
First available in Project Euclid: 10 July 2014

zbMATH: 1298.47046
MathSciNet: MR3263539
Digital Object Identifier: 10.35834/mjms/1404997105

Primary: 47B38
Secondary: ‎30H05 , 47B15 , 47B33

Keywords: bounded operators , ‎compact‎ ‎operators , Composition operators , generalized weighted Nevanlinna class , radial weight function , weighted Bergman spaces

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

Vol.26 • No. 1 • May 2014
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