Authors: Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Weighted composition operators from H∞ to the bloch space on the polydisc
Journal: Abstract and Applied Analysis
Volume: 2007
Issue Date: 2-Jul-2007
Rank: M23
ISSN: 1085-3375
DOI: 10.1155/2007/48478
Let Dn be the unit polydisc of n, φ(z)=( φ1 (z),...,φn (z)) be a holomorphic self-map of Dn, and ψ(z) a holomorphic function on Dn . Let H( Dn) denote the space of all holomorphic functions with domain Dn, H∞ ( Dn) the space of all bounded holomorphic functions on Dn, and B( Dn) the Bloch space, that is, B( Dn)={ f∈H( Dn) |||f|| B =| f(0) |+ sup z∈Dn ∑ k=1 n | (∂f/ ∂zk)(z) | ( 1- | zk | 2)<+∞ } . We give necessary and sufficient conditions for the weighted composition operator ψCφ induced by φ(z) and ψ(z) to be bounded and compact from H∞ ( Dn) to the Bloch space B( Dn).
Publisher: Hindawi
Project: NNSF of China (no.10671115)
PhD Foundation (no. 20060560002)
NSF of Guangdong Province (no. 06105648)

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