Authors: Stević, Stevo 
Chen, Renyu
Zhou, Zehua
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Weighted composition operators between Bloch-type spaces in the polydisc
Journal: Sbornik Mathematics
Volume: 201
Issue: 2
First page: 289
Last page: 319
Issue Date: 1-Jan-2010
Rank: M22
ISSN: 1064-5616
DOI: 10.1070/SM2010v201n02ABEH004073
Abstract: 
For p > 0, let βp(Dn) denote the p-Bloch space on the unit polydisc Dn of Cn and ρ(z) = (ρ1(z), ⋯ , ρn(z)) a holomorphic self-map of Dn. We investigate the boundedness and compactness of the weighted composition uCρf(z) = u(z)f(∞(z)) between p-Bloch space βp(Dn) (little p-Bloch space β 0p (Dn)) and q-Bloch space Bq(Dn) (little q-Bloch space β0q(Dn)). The most important result in the paper is that conditions for the compactness are different for the cases p ∈ (0, 1) and p ≥ 1, unlike for the case of the weighted operators on the unit disc.
Keywords: Bloch-type spaces | Boundedness | Compactness | Polydisc | Weighted composition operator
Publisher: Turpion

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