Stević-Sharma Operator on Spaces of Vector-Valued Holomorphic Functions

被引：0
作者：
Zeng Fan
Xin Guo
机构：
[1] School of Mathematics and Statistics,
[2] Xinyang Normal University,undefined
[3] School of Mathematics and Statistics,undefined
[4] Wuhan University,undefined
来源：
Complex Analysis and Operator Theory | 2022年 / 16卷
关键词：
Stević-Sharma operator; Vector-valued; Bergman space; Primary 47B38; 47B33; Secondary 30H05; 46E15;
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摘要：
In this paper, we are interested in the Stević-Sharma operator on the spaces of vector-valued holomorphic functions, which has never been considered so far. We completely characterize the boundedness of the Stević-Sharma operator between weak and strong vector-valued Bergman spaces in terms of a Julia-Carathéodory type function theoretic characterization and a power type characterization. Furthermore, we establish an interesting result: the boundedness of the Stević-Sharma operator between weak and strong vector-valued Bergman spaces is not only equivalent to the Hilbert-Schmidtness but also equivalent to the order boundedness of the Stević-Sharma operator between scalar value Bergman spaces.
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