与薛定谔型算子相关的Riesz变换的端点估计  

Endpoint Estimates for Riesz Transforms Related to Schrodinger Type 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》2020年第17期247-250,共4页Mathematics in Practice and Theory

摘　　要：假设薛定谔型算子L2=(-Δ)^2+V^2中的非负位势函数V属于反向H?lder函数类RHs(s>n/2),本文证明了与L2相关的Riesz变换T(α,β)=V^(2α)L2^(-β)(0<α≤β≤1)是L^1(R^n)到L^(n/n-4(β-α))(R^n)的有界算子.这个结论实质性地推广了已知结果.Let L2=(-Δ)2+V2 be the Schrodinger type operator and the nonnegative potential V belong to the reverse Holder class RHs with s>n/2.In this paper,we prove that the Riesz transform Tα,β=V2αL2-β(0<α≤β≤1)is bounded from L1(Rn)to Ln/n-4(β-α)(Rn).These results generalize substantially some known results.

关 键 词：薛定谔算子 反向Holder类 RIESZ变换 

分 类 号：O177[理学—数学]