Weighted estimates for powers and Smoothing estimates of Schrödinger operators with inverse-square potentials

Published 7 Sep 2016 in math.AP | (1609.01938v2)

Abstract: 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 $e^{{it\mathcal{L}_a}$.}