Acta mathematica scientia, Series B >
AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES
Received date: 2013-04-02
Online published: 2014-07-20
Supported by
Project supported by the National Natural Science Foundation of China (11171255, 11101279) and the Natural Science Foundation of Shanghai (13ZR1444100).
In this paper, we define the generalized counting functions in the higher dimen-sional 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.
Key words： essential norm; composition operator; weighted Bergman space
CHEN Zhi-Hua , JIANG Liang-Mei , YAN Qi-Ming . AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1145 -1156 . DOI: 10.1016/S0252-9602(14)60075-8
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