Subcritical approach to sharp Hardy-Littlewood-Sobolev type inequalities on the upper half space

被引：39

作者：

Doe, Jingbo ^{[1
]}

Guo, Qianqiao ^{[2
]}

Zhu, Meijun ^{[3
]}

机构：

[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China

[2] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Shaanxi, Peoples R China

[3] Univ Oklahoma, Dept Math, Norman, OK 73019 USA

来源：

ADVANCES IN MATHEMATICS | 2017年 / 312卷

基金：

中国国家自然科学基金;

关键词：

Subcritical approach; Sharp Hardy-Littlewood-Sobolev inequality; Best constant;

D O I：

10.1016/j.aim.2017.03.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and Yan in [6]) by introducing a uniform approach. The extremal functions are classified via the method of moving spheres, and the best constants are computed. The new approach can also be applied to obtain the classical HLS inequality and other similar inequalities. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1 / 45

页数：45

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