Weighted Composition Operators on Some Weighted Spaces in the Unit Ball. (9th June 2008)

• Record Type: Journal Article
• Authors: Fu, Xiaohong; Zhu, Xiangling
• Other Names: Stevic Stevo Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2008(2008)
• Publication Date: 2008-06-09
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2008/605807
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let𝔹 n be the unit ball ofℂ n, H ( 𝔹 n ) the space of all holomorphic functions in𝔹 n . Letu 𝛜 H ( 𝔹 n ) andα be a holomorphic self-map of𝔹 n . Forf 𝛜 H ( 𝔹 n ), the weigthed composition operatoru C α is defined by( u C α f ) ( z ) = u ( z ) f ( α ( z ) ), z 𝛜 𝔹 n . The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.