与高阶薛定谔算子相关的Riesz变换的弱型估计  

Weak Type Estimates of Riesz Transform Associated with Higher-Order Schrödinger Operators

作　　者：王艳烩 WANG Yan-hui(Department of Basic Science,Jiaozuo University,Jiaozuo 454003,China)

机构地区：[1]焦作大学基础科学系,河南焦作454003

出　　处：《数学的实践与认识》2025年第3期205-210,共6页Mathematics in Practice and Theory

基　　金：河南省自然科学基金(232300421142)。

摘　　要：假设m为非负整数且n≥2^(m+1)+1,考虑R^(n)上的高阶薛定谓算子H_(2^(m))=(-△)^(2^(m))+V^(2^(m)).当位势函数V属于反向Hölder函数类RH_(s)(n/2≤s<2^(m)n/2^(m+1)-j),同时也属于与(-Δ)^(2^(m))相关的高斯函数类时,得到了Riesz变换▽^jH_(2^(m))^(-2j/2^(m+1))(j=1,2,…,2^(m+1)-1)的弱型估计.Let m be a nonnegative integer and n≥2^(m+1)+1.In this paper,the higher order Schrodinger type operator H_(2^(m))=(-△)^(2^(m))+V^(2^(m))is considered on R^(n),and the weak type estimate of ies transform▽^jH_(2^(m))^(-2j/2^(m+1))(j=1,2,…,2^(m+1)-1)is estabished,here the nonnegative potential V belongs to both the reverse Hölder class RH_(s)for(n/2≤s<2^(m)n/2^(m+1)-j),and the Gaussian class associated with (-Δ)^(2^(m)).

关 键 词：薛定谔算子 反向Holder类 RIESZ变换 

分 类 号：O174.2[理学—数学]