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

页码：651 / 687

页数：37

共 37 条

[1] [Anonymous], 1970, SINGULAR INTEGRALS D
[2] SHARP SOBOLEV INEQUALITIES ON THE SPHERE AND THE MOSER-TRUDINGER INEQUALITY
BECKNER, W
[J]. ANNALS OF MATHEMATICS, 1993, 138 (01) : 213 - 242
[3] Brascamp H. J., 1974, J FUNCT ANAL, V17, P227
[4] BREZIS H, 1979, J MATH PURE APPL, V58, P137
[5] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[6] Brezis H., 1992, PARTIAL DIFFERENTIAL, P38
[7] Positive solutions of nonlinear problems involving the square root of the Laplacian
Cabre, Xavier
Tan, Jinggang
[J]. ADVANCES IN MATHEMATICS, 2010, 224 (05) : 2052 - 2093
[8] An extension problem related to the fractional Laplacian
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1245 - 1260
[9] Fractional Laplacian in conformal geometry
Chang, Sun-Yung Alice
del Mar Gonzalez, Maria
[J]. ADVANCES IN MATHEMATICS, 2011, 226 (02) : 1410 - 1432
[10] Chen W., 2011, ARXIV11102539

← 1 2 3 4 →