Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials
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- 作者：The Anh Bui<sup>asup><sup> ; sup><sup>the.bui@mq.edu.ausup><sup> ; sup><sup>bt_anh80@yahoo.comsup> ; Piero D'Ancona<sup>bsup><sup> ; sup><sup>dancona@mat.uniroma1.itsup> ; Xuan Thinh Duong<sup>asup><sup> ; sup><sup>xuan.duong@mq.edu.ausup> ; Ji Li<sup>asup><sup> ; sup><sup>ji.li@mq.edu.ausup> ; Fu Ken Ly<sup>csup><sup> ; sup><sup>ken.ly@sydney.edu.ausup>
- 关键词：35P25 ; 35Q55
- 刊名：Journal of Differential Equations
- 出版年：2017
- 出版时间：5 February 2017
- 年：2017
- 卷：262
- 期：3
- 页码：2771-2807
- 全文大小：431 K
- 卷排序：262
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.