Weighted composition operators from α-bloch space to H∞ on the polydisc

被引：80
|
作者：
Li, Songxiao
Stevic, Stevo
机构：
[1] Serbian Acad Sci, Inst Math, Belgrade 11000, Serbia
[2] JiaYing Univ, Dept Math, Meizhou, Guangdong, Peoples R China
[3] Shantou Univ, Dept Math, Meizhou, Guangdong, Peoples R China
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2007年 / 28卷 / 7-8期
基金：
中国国家自然科学基金;
关键词：
Bloch space; boundedness; compactness; weighted composition operator;
D O I：
10.1080/01630560701493222
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let D-n be the unit polydisc of C-n,phi(z)=(phi(1)( z), . . . ,phi(n)(z)) be a holomorphic self-map of Dn, and psi( z) a holomorphic function on D-n. Let H-infinity(D-n) be the space of all bounded holomorphic functions on D-n and B-alpha(D-n) the alpha-Bloch space. Necessary and suffcient conditions for the weighted composition operator psi C-phi induced by phi(z) and psi( z) to be bounded and compact from B-alpha(D-n)to H-infinity(D-n)are given in this paper. One of our results corrects and extends Theorem 1 in the paper by S. Ohno, Weighted composition operators between H-infinity and the Bloch space, Taiwanese.
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页码：911 / 925
页数：15
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