## Missouri Journal of Mathematical Sciences

### Composition Operators on Generalized Weighted Nevanlinna Class

Waleed Al-Rawashdeh

#### Abstract

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.

#### Article information

Source
Missouri J. Math. Sci., Volume 26, Issue 1 (2014), 14-22.

Dates
First available in Project Euclid: 10 July 2014

https://projecteuclid.org/euclid.mjms/1404997105

Digital Object Identifier
doi:10.35834/mjms/1404997105

Mathematical Reviews number (MathSciNet)
MR3263539

Zentralblatt MATH identifier
1298.47046

#### Citation

Al-Rawashdeh, Waleed. Composition Operators on Generalized Weighted Nevanlinna Class. Missouri J. Math. Sci. 26 (2014), no. 1, 14--22. doi:10.35834/mjms/1404997105. https://projecteuclid.org/euclid.mjms/1404997105

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