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

• Published in: Acta mathematica scientia Vol. 29; no. 5; pp. 1430 - 1438
• Main Author: 王雄亮 刘太顺
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2009; Department of Mathematics, University of Science and Technology of China, Hefei 230026, China%Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China
• Subjects: 30D45; 42B30; 47B33; Bloch空间; boundedness; compactness; composition type operators; Hardy spaces; Hardy空间; μ-Bloch spaces; 充分条件; 单位球; 德州仪器; 组合型; 组成型; 经营者; 42B30; μ-Bloch spaces; Hardy spaces; compactness; 47B33; boundedness; 30D45; composition type operators
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(09)60115-6

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.