AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to...

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Bibliographic Details
Published in:Acta mathematica scientia 2014-07, Vol.34 (4), p.1145-1156
Main Author: 陈志华 江良英 颜启明
Format: Article
Language:English
Subjects:
32H02
47B33
47B38
composition operator
Counting
essential norm
Functions (mathematics)
Mathematical analysis
Norms
Operators
Upper bounds
weighted Bergman space
上界
充分条件
加权Bergman空间
单位球
复合算子
本性范数
计数功能
运营商
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Description
Summary:In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(14)60075-8