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arXiv · 1609.01938

Weighted estimates for powers and Smoothing estimates of Schr\"odinger operators with inverse-square potentials

The Anh Bui·Piero D'Ancona·Xuan Thinh Duong·Ji Li·Fu Ken Ly
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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 $e^{it\mathcal{L}_a}$.

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The Anh Bui, Piero D'Ancona, Xuan Thinh Duong, Ji Li, Fu Ken Ly. 2016-09-07. Weighted estimates for powers and Smoothing estimates of Schr\"odinger operators with inverse-square potentials. https://arxiv.org/abs/1609.01938

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