Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

Abstract

We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let LV=−Δ+V(x) where Δ is the usual Laplacian on Rn and V(x)=V0(θ)r−2 where r=|x|,θ=x/|x| and V0(θ)∈C1(Sn−1) is a real function such that the operator −Δθ+V0(θ)+(n−2)2/4 is a strictly positive operator on L2(Sn−1). We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator LV.