Weighted estimates for powers and smoothing estimates of Schrodinger operators with inverse-square potentials

被引：12

作者：

The Anh Bui ^{[1
]}

D'Ancona, Piero ^{[2
]}

Xuan Thinh Duong ^{[1
]}

Li, Ji ^{[1
]}

Ly, Fu Ken ^{[3
]}

机构：

[1] Macquarie Univ, Dept Math, N Ryde, NSW 2109, Australia

[2] Sapienza Univ Roma, Dipartimento Matemat, Piazzale A Moro 2, I-00185 Rome, Italy

[3] Univ Sydney, Math Learning Ctr, Sydney, NSW 2006, Australia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Inverse-square potential; Littlewood-Paley theory; Heat kernel estimate; Negative power; Smoothing estimate; ELLIPTIC-OPERATORS; TIME DECAY; EQUATIONS; WAVE; INEQUALITIES;

D O I：

10.1016/j.jde.2016.11.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let L-a be a Schrodinger operator with inverse square potential a |x|(-2) on R-d, d >= 3. The main aim of this paper is to prove weighted estimates for fractional powers of L-a. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to L-a. As an application, we obtain smoothing estimates regarding the propagator e(itLa). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：2771 / 2807

页数：37

共 34 条

[1]

[Anonymous], 2000, GRAD STUD MATH

[2]

[Anonymous], 1985, Weighted Norm Inequalities and Related Topics

[3] Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights [J].

Auscher, Pascal ;

Martell, Jose Maria .

ADVANCES IN MATHEMATICS, 2007, 212 (01) :225-276

[4] Some dispersive estimates for Schrodinger equations with repulsive potentials [J].

Barcelo, Juan A. ;

Ruiz, Alberto ;

Vega, Luis .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 236 (01) :1-24

[5] New abstract Hardy spaces [J].

Bernicot, Frederic ;

Zhao, Jiman .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (07) :1761-1796

[6]

Burq N, 2004, INDIANA U MATH J, V53, P1665

[7] Strichartz estimates for the wave and Schrodinger equations with the inverse-square potential [J].

Burq, N ;

Planchon, F ;

Stalker, JG ;

Tahvildar-Zadeh, AS .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 203 (02) :519-549

[8] Weighted Lp estimates for powers of selfadjoint operators [J].

Cacciafesta, Federico ;

D'Ancona, Piero .

ADVANCES IN MATHEMATICS, 2012, 229 (01) :501-530

[9] Kato Smoothing and Strichartz Estimates for Wave Equations with Magnetic Potentials [J].

D'Ancona, Piero .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 335 (01) :1-16

[10] Evolution Equations on Non-Flat Waveguides [J].

D'Ancona, Piero ;

Racke, Reinhard .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 206 (01) :81-110

← 1 2 3 4 →