## Taiwanese Journal of Mathematics

### ON A CLASS OF OPERATORS FROM WEIGHTED BERGMAN SPACES TO SOME SPACES OF ANALYTIC FUNCTIONS

Zhi Jie Jiang

#### Abstract

Let $\mathbb D = \{ z \in \mathbb C: |z| \lt 1\}$ be the open unit disk in the complex plane $\mathbb C$, $H(\mathbb D)$ be the space of all analytic functions on $\mathbb D$, $\varphi$ be an analytic self-map of $\mathbb D$ and $u \in H(\mathbb D)$. Define operators by $DW_{\varphi,u}f = (u \cdot f \circ \varphi)'$ and $W_{\varphi,u}Df = (u \cdot f' \circ \varphi)$ for $f \in H(\mathbb D)$. In this paper we characterize bounded operators $DW_{\varphi,u}$ and $W_{\varphi,u}D$ from weighted Bergman space to Zygmund-type space, Bloch-type space and Bers-type space on the open unit disk. We also give some sufficient and necessary conditions for these operators to be compact operators in terms of inducing maps $\varphi$ and $u$.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 5 (2011), 2095-2121.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406425

Digital Object Identifier
doi:10.11650/twjm/1500406425

Mathematical Reviews number (MathSciNet)
MR2880395

Zentralblatt MATH identifier
1264.47035

#### Citation

Jiang, Zhi Jie. ON A CLASS OF OPERATORS FROM WEIGHTED BERGMAN SPACES TO SOME SPACES OF ANALYTIC FUNCTIONS. Taiwanese J. Math. 15 (2011), no. 5, 2095--2121. doi:10.11650/twjm/1500406425. https://projecteuclid.org/euclid.twjm/1500406425

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