多圆盘重调和Hardy空间上Toeplitz算子的交换性  

Commutativity of Toeplitz operators on pluriharmonic Hardy space of polydisk

作　　者：刘元[1] 丁宣浩[2] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]重庆工商大学数学与统计学院,重庆400067

出　　处：《桂林电子科技大学学报》2012年第5期406-409,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(10871217)

摘　　要：引入多圆盘重调和Hardy空间,并研究该空间上Toeplitz算子的交换性。首先给出多圆盘重调和Hardy空间的Toeplitz的算子定义、再生核公式,然后采用比较分析的方法研究Toeplitz算子的性质。研究结果显示:解析Toeplitz算子的半交换子与交换子不一定为0;解析Toeplitz算子的半交换子为0时,其中任何一个因子的符号可以不为常数;解析Toeplitz的交换子为0时,2个因子的符号的线性组合不一定是常数。可见,多圆盘重调和Hardy空间的Toeplitz算子是可交换的。The pluriharmonic Hardy space of the polydisk was introduced and its Toeplitz operator was studied.The definition of Toeplitz operator and its formula for regeneration nuclear were given,then the properties of Toeplitz operator were studied by the comparative analysis method.The results of the study show that the semi-commutator and commutator of two analytic Toeplitz operators are not always zero,and the semi-commutator of two analytic Toeplitz operators is zero but maybe neither of their symbols is constant,and the commutator of two analytic Toeplitz operators is zero but maybe their symbols＇ nontrivial linear combination is not constant.So the Toeplitz operator is commutative.

关 键 词：重调和Hardy空间 TOEPLITZ算子 多圆盘 交换子 

分 类 号：O177.1[理学—数学]