## Abstract and Applied Analysis

### On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

#### Abstract

Let $\mathbb{B}$ denote the open unit ball of ${\mathbb{C}}^{n}$. For a holomorphic self-map $\varphi$ of $\mathbb{B}$ and a holomorphic function $g$ in $\mathbb{B}$ with $g(0)=0$, we define the following integral-type operator: ${I}_{\varphi }^{g}f(z)={\int\,\!}_{0}^{1}\mathfrak{R}f(\varphi (tz))g(tz)(dt/t)$, $z\in \mathbb{B}$. Here $\mathfrak{R}f$ denotes the radial derivative of a holomorphic function $f$ in $\mathbb{B}$. We study the boundedness and compactness of the operator between Bloch-type spaces ${\mathcal{B}}_{\omega }$ and ${\mathcal{B}}_{\mu }$, where $\omega$ is a normal weight function and $\mu$ is a weight function. Also we consider the operator between the little Bloch-type spaces ${\mathcal{B}}_{\omega ,0}$ and ${\mathcal{B}}_{\mu ,0}$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 214762, 14 pages.

Dates
First available in Project Euclid: 1 November 2010

https://projecteuclid.org/euclid.aaa/1288620729

Digital Object Identifier
doi:10.1155/2010/214762

Mathematical Reviews number (MathSciNet)
MR2660388

Zentralblatt MATH identifier
1200.32005

#### Citation

Stević, Stevo; Ueki, Sei-Ichiro. On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball. Abstr. Appl. Anal. 2010 (2010), Article ID 214762, 14 pages. doi:10.1155/2010/214762. https://projecteuclid.org/euclid.aaa/1288620729