与高阶Schrodinger型算子相关的变分算子的Lipschitz交换子  

Lipschitz Commutators of Variation Operators Associated with High Order Schrodinger Type Operators

作　　者：孟晓燕[1] 赵凯 MENG Xiaoyan;ZHAO Kai(Department of Mathematics,Qingdao Huanghai University,Qingdao 266427,Shandong Province,China;School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Shandong Province,China)

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

出　　处：《吉林大学学报（理学版）》2021年第5期1071-1079,共9页Journal of Jilin University:Science Edition

基　　金：山东省自然科学基金(批准号:ZR2020MA004);国家自然科学基金(批准号:11471176,11871293).

摘　　要：设L=(-Δ)^(2)+V^( 2)是ℝn(n≥5)上的高阶Schrodinger型算子,其中非负位势V属于反向Holder类RH q(q>n/2).记Vρ(e-t L)为与高阶Schr dinger型算子L相关的变分算子.基于Herz型Hardy空间的原子分解理论,利用Schrodinger型算子的性质,证明该类变分算子与Lipschitz函数构成的交换子的L q有界性,并进一步证明该类变分算子的交换子从Herz型Hardy空间到Herz空间是有界的,在Morrey-Herz空间上也是有界的.Let L=(-Δ)^(2)+V ^(2) be a high order Schrodinger type operator in ℝn(n≥5), where a nonnegative potential V belongs to the reverse Holder class RHq(q>n/2). Let Vρ(e-tL) be the variation operator associated with the high order Schrodinger type operator L. Based on the theory of atomic decompesitions of Herz type Hardy spaces, by using the properties of the Schrodinger type operators, the boundedness of the commutators composed by such variation operators and Lipschitz fuctions on Lq is proved. Furthermore, it is proved that the commutators of this kind of variation operators are bounded from Herz type Hardy spaces to the Herz spaces and are bounded on Morrey-Herz spaces.

关 键 词：变分算子 Schrodinger型算子 交换子 HERZ型空间 有界性 

分 类 号：O174.2[理学—数学]