Toeplitz Operators with Quasihomogeneous Symbols on the Dirichlet Space of B_n  

作　　者：Hongzhao LIN Bo ZHANG Yufeng LU 

机构地区：[1]Department of Mathematics,Dalian University of Technology [2]Department of Computer and information,Fujian Agriculture and Forestry University [3]Department of Science,Dalian Ocean University

出　　处：《Journal of Mathematical Research with Applications》2013年第6期717-731,共15页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.11271059)

摘　　要：In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator.In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator.

关 键 词：Dirichlet space unit ball Toeplitz operators quasihomogeneous symbols. 

分 类 号：O177[理学—数学]