  We study the uniform resolvent estimates for Schr\"odinger operator with a
Hardy-type singular potential.
  Let $\mathcal{L}_V=-\Delta+V(x)$ where $\Delta$ is the usual Laplacian on
$\mathbb{R}^n$ and $V(x)=V_0(\theta) r^{-2}$ where $r=|x|, \theta=x/|x|$ and
$V_0(\theta)\in\mathcal{C}^1(\mathbb{S}^{n-1})$ is a real function such that
the operator $-\Delta_\theta+V_0(\theta)+(n-2)^2/4$ 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 $\mathcal{L}_V$.

Analysis of PDEs