Authors: Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Weighted composition operators from α-Bloch space to H ∞ on the polydisc
Journal: Numerical Functional Analysis and Optimization
Volume: 28
Issue: 7-8
First page: 911
Last page: 925
Issue Date: 1-Jul-2007
Rank: M23
ISSN: 0163-0563
DOI: 10.1080/01630560701493222
Abstract: 
Let double struk D signn be the unit polydisc of ℂn, φ(z) = (φ1(z), . . . , φn(z)) be a holomorphic self-map of double struk D sign n, and φ(z) a holomorphic function on double struk D sign n. Let H∞(double struk D signn) be the space of all bounded holomorphic functions on double struk D signn and script B sign(double struk D signn) the -Bloch space. Necessary and sufficient conditions for the weighted composition operator φC φ induced by φ(z) and φ(z) to be bounded and compact from script B sign(double struk D signn) to H∞(double struk D signn) 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∞ and the Bloch space, Taiwanese J. Math. 2001; 5:555-563.
Keywords: Bloch space | Boundedness | Compactness | Weighted composition operator
Publisher: Taylor & Francis
Project: NNSF of China (no. 10671115)
Specialized Research Fund for the doctoral program of Higher Education (no. 20060560002)
NSF of Guangdong Province (no. 06105648)

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