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

Letφ 1andφ 2be holomorphic self-maps of the open unit ball 𝔹 in ℂ N ,u 1andu2 be holomorphic functions on 𝔹 and let weighted composition operators W φ 1 , u 1 ; W φ 2 , u 2 : A α p → H v ∞ be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Ber...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 6; pp. 2647 - 2665
Main Authors Stević, Stevo, Jiang, Zhi Jie
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2011
Subjects
Abstract spaces
Analytic functions
Banach space
Topological compactness
Unit ball
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Summary:Letφ 1andφ 2be holomorphic self-maps of the open unit ball 𝔹 in ℂ N ,u 1andu2 be holomorphic functions on 𝔹 and let weighted composition operators W φ 1 , u 1 ; W φ 2 , u 2 : A α p → H v ∞ be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Bergman space A α p , 0 < p < ∞ , α > − 1 , to the weighted-type space H v ∞ of holomorphic functions on 𝔹 in terms of inducing symbolsφ 1,φ 2,u 1andu 2. For the casep> 1 we find an asymptotically equivalent expression to the essential norm of the operator. 2010Mathematics Subject Classification: Primary 47B38; Secondary 47B33, 47B37. Key words and phrases: Weighted composition operator, Weighted Bergman space, Weighted-type space, Essential norm, Compact operator.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406489