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

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.