SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE
SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE
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DOI：
10.1093/imrn/rnt213
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发表时间：
2013-09
影响因子：
1
通讯作者：
Jingbo Dou;Meijun Zhu
中科院分区：
文献类型：
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作者：
Jingbo Dou;Meijun Zhu
经典尖锐Hardy-Littlewood-Sobolev不等式的推广至少有两个方向：(1)在一般流形上推广尖锐不等式；(2)对负指数λ = n−α（即α > n）进行推广。本文通过在上半部空间（保形等效于球）上建立尖锐的Hardy-Littlewood-Sobolev不等式，证实了沿第一方向扩展的可能性。得到了极值函数的存在性；对于指数的一定范围，我们用移动球法对所有的极值函数进行了分类。
There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequality on the upper half space (which is conformally equivalent to a ball). The existences of extremal functions are obtained; And for certain range of the exponent, we classify all extremal functions via the method of moving sphere.