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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