非齐度量测度空间上广义分数次积分算子交换子的有界性  

Boundedness of Commutators of Generalized Fractional Integral Operators on Non-homogeneous Metric Measure Spaces

作　　者：张振荣[1] 赵凯 ZHANG Zhen-rong;ZHAO Kai(Department of Mathematics and Physics,Qingdao Huanghai University,Qingdao Shandong 266427,China;School of Mathematics and Statistics,Qingdao University,Qingdao Shandong 266071,China)

机构地区：[1]青岛黄海学院数理教学部,山东青岛266427 [2]青岛大学数学与统计学院,山东青岛266071

出　　处：《西南大学学报（自然科学版）》2020年第8期88-96,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471176,11871293)。

摘　　要：利用非齐度量测度空间的性质,应用分数次积分算子的有界性理论,基于非齐度量测度空间上Herz空间的刻画以及Herz型Hardy空间的原子分解和分子分解理论,证明了广义分数次积分算子与Lipschitz函数生成的交换子在非齐度量测度空间上的Herz空间和Herz型Hardy空间的有界性.In this paper,using the properties of the non-homogeneous metric measure spaces,applying the theory of boundedness for singular integral operators,and based on the characterization of Herz spaces and the atomic and molecular decompositions of Herz-type Hardy spaces with non-homogeneous metric measure,the boundedness of the commutators generated by the generalized fractional integral operators and Lipschitz functions on the Herz spaces and Herz-type Hardy spaces with non-homogeneous metric measure are proved.

关 键 词：非齐度量测度空间 广义分数次积分算子 交换子 有界性 

分 类 号：O174.2[理学—数学]