Sharp Hardy-Littlewood-Sobolev Inequality on the Upper Half Space

被引：63
|
作者：
Dou, Jingbo [1 ]
Zhu, Meijun [2 ]
机构：
[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China
[2] Univ Oklahoma, Dept Math, Norman, OK 73019 USA
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 03期
基金：
中国国家自然科学基金;
关键词：
YAMABE PROBLEM; MANIFOLDS; UNIQUENESS; EXISTENCE; CONSTANTS; THEOREMS;
D O I：
10.1093/imrn/rnt213
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The sharp Hardy-Littlewood-Sobolev inequality on the upper half space is proved. The existences of extremal functions are obtained. For certain exponent, we classify all extremal functions via the method of moving sphere, and compute the best constants for the sharp inequality.
引用
收藏
页码：651 / 687
页数：37
相关论文
共 50 条
  • [1] Sharp Reversed Hardy-Littlewood-Sobolev Inequality on the Half Space R+n
    Quoc Anh Ngo
    Van Hoang Nguyen
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2017, 2017 (20) : 6187 - 6230
  • [2] Subcritical approach to sharp Hardy-Littlewood-Sobolev type inequalities on the upper half space
    Doe, Jingbo
    Guo, Qianqiao
    Zhu, Meijun
    ADVANCES IN MATHEMATICS, 2017, 312 : 1 - 45
  • [3] CLASSIFICATION OF EXTREMAL FUNCTIONS TO LOGARITHMIC HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE
    Dou, Jingbo
    Li, Ye
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (08) : 3939 - 3953
  • [4] Weighted Hardy-Littlewood-Sobolev inequalities on the upper half space
    Dou, Jingbo
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (05)
  • [5] Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
    Frank, Rupert L.
    Lieb, Elliott H.
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (1-2) : 85 - 99
  • [6] Sharp reversed Hardy-Littlewood-Sobolev inequality on R n
    Quoc Anh Ngo
    Van Hoang Nguyen
    ISRAEL JOURNAL OF MATHEMATICS, 2017, 220 (01) : 189 - 223
  • [7] Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality
    WU Di
    SHI ZuoShunHua
    YAN DunYan
    ScienceChina(Mathematics), 2014, 57 (05) : 963 - 970
  • [8] Sharp reversed Hardy-Littlewood-Sobolev inequality with extension kernel
    Dai, Wei
    Hu, Yunyun
    Liu, Zhao
    STUDIA MATHEMATICA, 2023, 271 (01) : 1 - 38
  • [9] Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality
    Wu Di
    Shi ZuoShunHua
    Yan DunYan
    SCIENCE CHINA-MATHEMATICS, 2014, 57 (05) : 963 - 970
  • [10] Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality
    Di Wu
    ZuoShunHua Shi
    DunYan Yan
    Science China Mathematics, 2014, 57 : 963 - 970
12345