文摘
Let LaLa be a Schrödinger operator with inverse square potential a|x|−2a|x|−2 on RdRd, d≥3d≥3. The main aim of this paper is to prove weighted estimates for fractional powers of LaLa. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to LaLa. As an application, we obtain smoothing estimates regarding the propagator eitLaeitLa.