广义Riesz变换高阶交换子的CBMO估计  

CBMO Estimates for Higher Order Commutators Generated by Generalized Riesz Transform Associated to Second Order Elliptic Operators

作　　者：钟海萍 周伟松[2] 张京友[3] 王兴武 ZHONG Haiping;ZHOU Weisong;ZHANG Jingyou;WANG Xingwu(Department of Natural Sciences, Yuzhang Normal University, Nanchang 330103, Jiangxi;Research Centre of System Theory and Application, Chongqing University of Post and Telecommunication, Chongqing 400065;College of Mathematics and Statistics, Chongqing Three Gorges University, Choagqing 404000)

机构地区：[1]豫章师范学院自然科学系,江西南昌330103 [2]重庆邮电大学系统理论与应用研究中心,重庆400065 [3]重庆三峡学院数学与统计学院,重庆404000

出　　处：《四川师范大学学报（自然科学版）》2018年第4期510-515,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：江西省教育厅科学技术研究项目(GJJ151325)

摘　　要：主要研究高阶交换子R_L^(b,m)的CBMO估计,利用对函数进行环形分解和对算子转化为相应的截断算子的方法,得到R_L^(b,m)从MK_(p,q1)^(α1,λ)(R^n)空间到MK_(p,q2)^(α2,λ)(R^n)空间的有界性.其次,利用椭圆算子相伴的热核具有L^2off-diagonal估计,得到广义Riesz变换R_L从MK_(p,q1)^(α1,λ)(R^n)空间到MK_(p,q2)^(α2,λ)(R^n)空间的有界性.将Riesz变换相关结论做了进一步推广.The boundedness for the higher order commutators Rb,mLgenerated by generalized Riesz transform RLand CBMO functions is studied. We prove that Rb,mLis bounded from MK（p,q1）^α1,λ（R^n）spaces to MK（p,q2）^α2,λ（R^n） spaces. Moreover,the boundedness of RLfrom MK（p,q1）^α1,λ（R^n） spaces to MK（p,q2）^α2,λ（R^n） spaces is also established,when the heat kernel associated to L has L^2 off-diagonal estimates. The relevant conclusions of Riesz transform are further generalized.

关 键 词：圆算子 广义Riesz变换 MORREY-HERZ空间 CBMO空间 L2off-diagonal估计 

分 类 号：O174.2[理学—数学]