Weighted Composition Operators between Generally Weighted Bloch Spaces of Polydisk  

作　　者：LI Haiying LIU Peide 

机构地区：[1]College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China [2]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2010年第1期7-12,共6页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (10671147,10401027);the Key Project of Ministry of Education of China (208081);the Natural Science Foundation of Henan(2007110016;2008B110006)

摘　　要：Let φ be a holomorphic self-map of the open unit polydisk U nin C nand ψ a holomorphic function on U n,p,q0. ∨In this paper,we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and φ,sufficient conditions for the weighted composition operator Wψ,φ induced by ψ and φ to be bounded and compact between the generally weighted Bloch spaces are investigated.Let φ be a holomorphic self-map of the open unit polydisk U nin C nand ψ a holomorphic function on U n,p,q0. ∨In this paper,we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and φ,sufficient conditions for the weighted composition operator Wψ,φ induced by ψ and φ to be bounded and compact between the generally weighted Bloch spaces are investigated.

关 键 词：holomorphic self-map composition operator Bloch space generally weighted Bloch space 

分 类 号：O174.5[理学—数学] O178[理学—基础数学]