双线性Calderòn-Zygmund算子交换子在Triebel-Lizorkin空间上有界的充分必要条件  

Sufficient and necessary conditions for the boundedness of commutators of bilinear Calderòn-Zygmund operators on Triebel-Lizorkin Spaces

作　　者：房成龙 FANG Cheng-long(School of Mathematics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学数学学院,北京100872

出　　处：《东北师大学报（自然科学版）》2021年第1期7-13,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2016D01C381,2019D01C334);国家自然科学基金资助项目(11661075).

摘　　要：讨论了双线性Calderòn-Zygmund算子相关问题,证明了其与b_(1),b_(2)生成交换子从乘积Lebesgue空间到Triebel-Lizorkin空间有界的充分条件是b_(1),b_(2)为Lipschitz函数.同时证明了Calderòn-Zygmund算子交换子从乘积Lebesgue空间到Lebesgue空间、Triebel-Lizorkin空间有界的必要条件是b_(1)=b_(2)为Lipschitz函数.In this paper,it is shown that the sufficient conditions for the bound-boundedness of bilinear Calderòn-Zygmund operator and b_(1),b_(2)generating commutator from product Lebesgue space to Triebel-Lizorkin space to be b_(1),b_(2)as Lipschitz function.Next,it is proved that b_(1)=b_(2)is a necessary condition for Lipschitz function to be bounded from product Lebesgue space to Triebel-Lizorkin space for the commutator of bilinear Calderòn-Zygmund operator.

关 键 词：双线性Calderòn-Zygmund算子 交换子 LIPSCHITZ函数 LEBESGUE空间 TRIEBEL-LIZORKIN空间 

分 类 号：O174.2[理学—数学]