与高阶Schrodinger-型算子相关的变分算子在Herz-型空间的有界性  

Boundedness of the Variation Operators Associated with High-Order Schrodinger-Type Operators on the Herz-Type Spaces

作　　者：王晓燕[1] 赵凯 WANG Xiaoyan;ZHAO Kai(Department of Mathematics,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：《西南大学学报（自然科学版）》2021年第12期88-94,共7页Journal of Southwest University(Natural Science Edition)

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

摘　　要：设L=(-Δ)^(2)+V^(2)是R^(n)(n≥5)上的高阶Schrodinger-型算子,其中非负位势V属于反向H lder类RH q q>n 2.记V_(ρ)(e^(-t L))为与高阶Schrodinger-型算子L生成的热半群相关的变分算子,基于此类变分算子在L^(q)空间上有界的结果,应用Herz-型Hardy空间的原子分解理论,以及Schrodinger-型算子的性质,进行不等式的估计,证明了V_(ρ)(e^(-t L))是从Herz-型Hardy空间到Herz空间的有界算子,也是Morrey-Herz空间上的有界算子.Let L=(-Δ)^(2)+V^(2) be a high-order Schrodinger-type operator in R^(n)(n≥5),where V is a non-negative potential satisfying the reverse H lder inequality.Suppose that V_(ρ)(e^(-t L))is the variation operator associated with the high-order Schrodinger operator.Based on the boundedness of the variation operators on L^(q) spaces,and using the atomic decomposition of Herz-type Hardy spaces and the properties of the Schrodinger-type operators,the inequalities are estimated.The boundedness of the variation operators associated with the Schrodinger-type operators from Herz-type Hardy spaces into the Herz spaces is proved.The boundedness of the variation operators on Morrey-Herz spaces is also obtained.

关 键 词：变分算子 Schrodinger-型算子 Herz-型空间 有界性 

分 类 号：O174.2[理学—数学]