Composition Operator from Logarithmic Bloch-Type Space to Bergman Space on Unit Polydisc  

作　　者：张利 曾红刚 

机构地区：[1]School of Sciences,Tianjin University

出　　处：《Transactions of Tianjin University》2011年第6期450-453,共4页天津大学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (No.10971153)

摘　　要：In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.

关 键 词：composition operator logarithmic Bloch-type space Bergman space COMPACTNESS BOUNDEDNESS 

分 类 号：O177[理学—数学]