COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL  

作　　者：王雄亮 刘太顺 

机构地区：[1]Department of Mathematics, University of Science and Technology of China [2]Department of Mathematics, Huzhou Teachers College, Huzhou

出　　处：《Acta Mathematica Scientia》2009年第5期1430-1438,共9页数学物理学报（B辑英文版）

基　　金：Supported by NSF of China (10571164);SRFDP of Higher Education (20050358052)

摘　　要：Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.

关 键 词：Hardy spaces μ-Bloch spaces composition type operators BOUNDEDNESS COMPACTNESS 

分 类 号：O177[理学—数学]