与薛定谔算子相关的一类积分变换  

A Class of Integral Transformations Related to Schrodinger Operator

作　　者：何月香[1] 王月山[1] HE Yuexiang;WANG Yueshan(Basic Sciences Teaching Department,Jiaozuo University,Jiaozuo,Henan 454000,China)

机构地区：[1]焦作大学基础教学部,河南 焦作 454000

出　　处：《焦作大学学报》2022年第4期62-64,共3页Journal of Jiaozuo University

摘　　要：假设R^(n)(n≥3)上的薛定谔型算子L=-∆+V中的非负位势函数V属于反向Hölder类RH_(s),s≥n/2,对j=1,…,n,定义积分变换μ^(L)_(j)(f)(x)=(∫^(∞)_(0)|∫_(|x-y|≤t) K^(L)_(j)(x,y)f(y)dy|^(2)dt/t^(3))^(1/2),这里K^(L)_(j)(x,y)=K^(L)_(j)(x,y)|x-y|,K^(L)_(j)(x,y)是Riesz变换ə/əxjL^(1/2)的核函数。证明了积分变换μ^(L)_(j)在L^(p)(R^(n))空间上的有界性。Suppose that the non-negative potential function V in the Schrodinger type operator L=-∆+V on R^(n)(n≥3) belongs to the reverse Hölder class RH_(s),s≥n/2.For j=1,...,n,the integral transformation is defined as μ^(L)_(j)(f)(x)=(∫^(∞)_(0)|∫_(|x-y|≤t) K^(L)_(j)(x,y)f(y)dy|^(2)dt/t^(3))^(1/2)Here K^(L)_(j)(x,y)=K^(L)_(j)(x,y)|x-y|,K^(L)_(j)(x,y) is kernel function Riesz transformation ə/əxjL^(1/2).It is proved that the boundness of the integral transformation μ^(L)_(j) on the space of L^(p)(R^(n)).

关 键 词：薛定谔算子 反向Hölder类 RIESZ变换 

分 类 号：O177.6[理学—数学]