摘要
设L=(-Δ)^(2)+V^(2)是R^(n)(n≥5)上的高阶Schrödinger型算子,其中非负位势V属于反向Hölder类RHq(q>n/2).记Vp(e^(-tL)),为与高阶Schrödinger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Schrödinger型算子的性质,证明了这类变分算子与BMO函数构成的交换子是从HerzHardy空间到Herz空间有界的,也是在Morrey-Herz空间上有界的结果.
Let L=(-Δ)^(2)+V^(2) be a high order Schrödinger type operator in R^(n)(n≥5),where V is a nonnegative potential satisfying the reverse Hölder inequality,and Vρ(e^(-tL))be the variation operator associated with the high order Schrödinger type operator.Based on the theory of atomic decompesitions of Herz-Hardy spaces,using the properties of the Schrödinger type operators,the boundedness of the commutators composed by the variation operators associated with the Schrödinger type operators and BMO fuctions from Herz type Hardy spaces into the Herz spaces and the boundedness of the commutators on Morrey-Herz spaces are proved.
作者
姜伟伟
赵凯
JIANG Wei-wei;ZHAO Kai(Department of Mathematics,Qingdao Huanghai University,Qingdao 266427,Shandong,China;School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Shandong,China)
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第3期429-436,共8页
Journal of Yunnan University(Natural Sciences Edition)
基金
山东省自然科学基金(ZR2020MA004)
国家自然科学基金(11471176,11871293).
