## Abstract and Applied Analysis

### Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

#### Abstract

Let ${\mathbb{B}}_{n}$ be the unit ball of ${\mathbb{C}}^{n}$, $H({\mathbb{B}}_{n})$ the space of all holomorphic functions in ${\mathbb{B}}_{n}$. Let $u\in H({\mathbb{B}}_{n})$ and $\alpha$ be a holomorphic self-map of ${\mathbb{B}}_{n}$. For $f\in H({\mathbb{B}}_{n})$, the weigthed composition operator $u{C}_{\alpha }$ is defined by $(u{C}_{\alpha }f)(z)=u(z)f(\alpha (z)),z\in {\mathbb{B}}_{n}.$ The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 605807, 8 pages.

Dates
First available in Project Euclid: 9 September 2008

https://projecteuclid.org/euclid.aaa/1220969177

Digital Object Identifier
doi:10.1155/2008/605807

Mathematical Reviews number (MathSciNet)
MR2417227

Zentralblatt MATH identifier
1160.47024

#### Citation

Fu, Xiaohong; Zhu, Xiangling. Weighted Composition Operators on Some Weighted Spaces in the Unit Ball. Abstr. Appl. Anal. 2008 (2008), Article ID 605807, 8 pages. doi:10.1155/2008/605807. https://projecteuclid.org/euclid.aaa/1220969177

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