Weighted estimates for powers and Smoothing estimates of Schr\"odinger operators with inverse square potentials
Let \mathcal{L}_a$ be a Schr\"odinger operator with inverse square potential $a|x| 2} on \mathbb{R}^d, d\geq 3$ The main aim of this paper is to prove weighted estimates for fractional powers of \mathcal{L}_a$ The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to \mathcal{L}_a$ As an application, we obtain smoothing estimates regarding the propagator $e^{it\mathcal{L}_a}