Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Xiaohong Fu and Xiangling Zhu

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: Let 𝔹n be the unit ball of ℂn, H(𝔹n) the space of all holomorphic functions in 𝔹n. Let u𝞊H(𝔹n) and α be a holomorphic self‐map of 𝔹n. For f𝞊H(𝔹n), the weigthed composition operator uCα is defined by (uCαf)(z) = u(z)f(α(z)), z𝞊𝔹n. The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

Date: 2008
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