## Abstract and Applied Analysis

### Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces

#### Abstract

Let $H(\mathrm{\Bbb D})$ denote the space of all holomorphic functions on the unit disk $\mathrm{\Bbb D}$ of $\Bbb C$, $u\in H(\mathrm{\Bbb D})$ and let  n be a positive integer, $\phi$ a holomorphic self-map of $\mathrm{\Bbb D}$, and $\mu$ a weight. In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator ${\mathrm{\scr D}}_{\phi ,u}^{n}f(z)=u(z){f}^{(n)}(\phi (z)),f\in H(\mathrm{\Bbb D})$, from the logarithmic Bloch spaces to the Zygmund-type spaces.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 832713, 14 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276920

Digital Object Identifier
doi:10.1155/2014/832713

Mathematical Reviews number (MathSciNet)
MR3198257

Zentralblatt MATH identifier
07023157

#### Citation

Qu, Huiying; Liu, Yongmin; Cheng, Shulei. Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 832713, 14 pages. doi:10.1155/2014/832713. https://projecteuclid.org/euclid.aaa/1412276920

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