Authors: Stević, Stevo 
Jiang, Zhi Jie
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Compactness of the differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball
Journal: Taiwanese Journal of Mathematics
Volume: 15
Issue: 6
First page: 2647
Last page: 2665
Issue Date: 1-Jan-2011
Rank: M22
ISSN: 1027-5487
DOI: 10.11650/twjm/1500406489
Abstract: 
Let Φ1 and Φ2 be holomorphic self-maps of the open unit ball B in CN, u1 and u2 be holomorphic functions on B and let weighted composition operators W Φ1,u1; WΦ2,u2: Apα → H∞v be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Bergman space Apα, 0 < p < ∞, α >-1, to the weighted-type space H∞v of holomorphic functions on B in terms of inducing symbols Φ1, Φ2, u1 and u2. For the case p > 1 we find an asymptotically equivalent expression to the essential norm of the operator.
Keywords: Compact operator | Essential norm | Weighted bergman space | Weighted composition operator | Weighted-type space
Publisher: Mathematical Society of the Republic of China
Project: Science Foundation of Sichuan Province (No.09ZC115)

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