Achievability of a supremum for the Hardy-Littlewood-Sobolev inequality with supercritical exponent

被引：2
|
作者：
An, Xiaoming [1 ]
Peng, Shuangjie [1 ]
Xie, Chaodong [2 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
[2] Guizhou Univ Ethin Minor, Sch Econ Management, Guiyang 550025, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Hardy-Littlewood-Sobolev inequality; achievability of a supremum; supercritical exponent;
D O I：
10.1007/s11425-018-9484-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove that the supremum sup {integral(B)integral(B) vertical bar u(y)vertical bar(p(vertical bar y vertical bar))vertical bar u(x)vertical bar(p(vertical bar x vertical bar)) /vertical bar x - y vertical bar(mu) dxdy : u is an element of H-0,H- (1)(rad) (B), parallel to del u parallel to(L2(B)) = 1} is attained, where B denotes the unit ball in R-N (N >= 3), mu is an element of (0,N), p(r) = 2(mu)* + r(t), t is an element of (0, min{N/2 - mu/4, N - 2}) and 2(mu)* = (2N - mu)/(N - 2) is the critical exponent for the Hardy-Littlewood-Sobolev inequality.
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页码：2497 / 2504
页数：8
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