Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Norms of some operators on the Bergman and the Hardy space in the unit polydisk and the unit ball
Journal: Applied Mathematics and Computation
Volume: 215
Issue: 6
First page: 2199
Last page: 2205
Issue Date: 15-Nov-2009
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2009.08.014
Abstract: 
Let H (X) be the class of all holomorphic functions on the set X ⊂ Cn and u ∈ H (X). We calculate operator norms of the multiplication operators Mu (f) = uf, on the weighted Bergman space Aαp (X), as well as on the Hardy space Hp (X), where X is the unit polydisk Dn or the unit ball B in Cn. We also calculate the norm of the weighted composition operator from the weighted Bergman space Aover(α, →)p (Dn), over(α, →) > - 1, p > 0, and the Hardy space Hp (Dn), p > 0, to a weighted-type space on the unit polydisk.
Keywords: Hardy space | Multiplication operator | Operator norm | Polydisk | Unit ball | Weighted Bergman space | Weighted composition operator
Publisher: Elsevier

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