Taiwanese Journal of Mathematics

COMPACTNESS OF THE DIFFERENCES OF WEIGHTED COMPOSITION OPERATORS FROM WEIGHTED BERGMAN SPACES TO WEIGHTED-TYPE SPACES ON THE UNIT BALL

Stevo Stević and Zhi Jie Jiang

Full-text: Open access

Abstract

Let $\varphi_{1}$ and $\varphi_{2}$ be holomorphic self-maps of the open unit ball $\mathbb B$ in $\mathbb C^N$, $u_{1}$ and $u_{2}$ be holomorphic functions on $\mathbb B$ and let weighted composition operators $W_{\varphi_{1},u_{1}}$; $W_{\varphi_{2},u_{2}}: A^{p}_{\alpha} \to H^{\infty}_{v}$ be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Bergman space $A^p_\alpha$, $0-1$, to the weighted-type space $H^\infty_v$ of holomorphic functions on $\mathbb B$ in terms of inducing symbols $\varphi_{1}$, $\varphi_{2}$, $u_{1}$ and $u_{2}$. For the case $p \gt 1$ we find an asymptotically equivalent expression to the essential norm of the operator.

Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2647-2665.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406489

Digital Object Identifier
doi:10.11650/twjm/1500406489

Mathematical Reviews number (MathSciNet)
MR2896136

Zentralblatt MATH identifier
1315.47034

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 47B33: Composition operators 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
weighted composition operator weighted Bergman space weighted-type space essential norm compact operator

Citation

Stević, Stevo; Jiang, Zhi Jie. COMPACTNESS OF THE DIFFERENCES OF WEIGHTED COMPOSITION OPERATORS FROM WEIGHTED BERGMAN SPACES TO WEIGHTED-TYPE SPACES ON THE UNIT BALL. Taiwanese J. Math. 15 (2011), no. 6, 2647--2665. doi:10.11650/twjm/1500406489. https://projecteuclid.org/euclid.twjm/1500406489


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