Uniform resolvent estimates for Schr\"odinger operator with an inverse-square potential

We study the uniform resolvent estimates for Schr"odinger operator with a Hardy-type singular potential. Let ${\mathcal{L}}_V=-\mathrm{\Delta }+V(x)$ where $\mathrm{\Delta }$ is the usual Laplacian on ${\mathbb{R}}^n$ and $V(x)=V_0(\theta )r^{-2}$ where $r=\mathrm{\mid }x\mathrm{\mid },\theta =x\mathrm{/}\mathrm{\mid }x\mathrm{\mid }$ and $V_0(\theta )\in {\mathcal{C}}^1({\mathbb{S}}^{n-1})$ is a real function such that the operator $-{\mathrm{\Delta }}_{\theta }+V_0(\theta )+(n-2{)}^2\mathrm{/}4$ is a strictly positive operator on $L^2({\mathbb{S}}^{n-1})$. We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator ${\mathcal{L}}_V$.