Taiwanese Journal of Mathematics

PRODUCTS OF MULTIPLICATION, COMPOSITION AND DIFFERENTIATION OPERATORS FROM MIXED-NORM SPACES TO WEIGHTED-TYPE SPACES

Fang Zhang and Yongmin Liu

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Abstract

Let $\varphi$ be an analytic self-map of the unit disk $\mathbb{D}$, $H(\mathbb{D})$ the space of analytic functions on $\mathbb{D}$ and $\psi_{1},\psi_{2}\in H(\mathbb{D})$. Recently Stevi$\acute{\hbox{c}}$ and co-workers defined the following operator $$T_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_{1}(z)f(\varphi(z))+\psi_{2}(z)f'(\varphi(z)),\ \ \ f\in H(\mathbb{D}).$$ The boundedness and compactness of the operators $T_{\psi_{1},\psi_{2},\varphi}$ from mixed-norm spaces to weighted-type spaces are investigated in this paper.

Article information

Source
Taiwanese J. Math., Volume 18, Number 6 (2014), 1927-1940.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500667504

Digital Object Identifier
doi:10.11650/tjm.18.2014.4311

Mathematical Reviews number (MathSciNet)
MR3284039

Zentralblatt MATH identifier
1357.47037

Subjects
Primary: 47B38: Operators on function spaces (general) 47B33: Composition operators 46E14 30H10: Hardy spaces

Keywords
multiplication operator differentiation operator composition operator mixed-norm space weighted-type space

Citation

Zhang, Fang; Liu, Yongmin. PRODUCTS OF MULTIPLICATION, COMPOSITION AND DIFFERENTIATION OPERATORS FROM MIXED-NORM SPACES TO WEIGHTED-TYPE SPACES. Taiwanese J. Math. 18 (2014), no. 6, 1927--1940. doi:10.11650/tjm.18.2014.4311. https://projecteuclid.org/euclid.twjm/1500667504


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