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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