Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Weighted composition operators from the logarithmic weighted-type space to the weighted Bergman space in Cn | Journal: | Applied Mathematics and Computation | Volume: | 216 | Issue: | 3 | First page: | 924 | Last page: | 928 | Issue Date: | 1-Apr-2010 | Rank: | M21 | ISSN: | 0096-3003 | DOI: | 10.1016/j.amc.2010.01.105 | Abstract: | Let Ω be a bounded, circular, strictly convex domain in Cn with C2 boundary and H (Ω) the space of all analytic functions on Ω. Let u ∈ H (Ω) and φ be a holomorphic self-map of Ω. The weighted composition operator uCφ on H (Ω) is defined by (uCφ) (f) (z) = u (z) f (φ (z)), where f ∈ H (Ω) and z ∈ Ω. Let Hlogγβ (Ω), β > 0, γ ∈ R+, be the logarithmic weighted-type space on Ω, and Aαp (Ω), p ∈ (0, ∞), α ∈ (- 1, ∞), the weighted Bergman space on Ω. Here we characterize the boundedness and compactness of the weighted composition operator uCφ : Hlogγβ (Ω) → Aαp (Ω). |
Keywords: | Bergman space | Bounded circular domain | Boundedness | Compactness | Primary 47B38 | Secondary 47B33 | The logarithmic weighted-type space | Weighted composition operator | Publisher: | Elsevier |
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