Improved Hardy–Littlewood–Sobolev Inequality on S^(n)under Constraints  

作　　者：Yun Yun HU Jing Bo DOU 

机构地区：[1]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第11期2149-2163,共15页数学学报（英文版）

基　　金：the National Science Foundation of China(Grant Nos.12101380,12071269);China Postdoctoral Science Foundation(Grant No.2021M700086);Youth Innovation Team of Shaanxi Universities and the Fundamental Research Funds for the Central Universities(Grant Nos.GK202307001,GK202202007)。

摘　　要：In this paper,we establish an improved Hardy–Littlewood–Sobolev inequality on Snunder higher-order moments constraint.Moreover,by constructing precise test functions,using improved Hardy–Littlewood–Sobolev inequality on S^(n),we show such inequality is almost optimal in critical case.As an application,we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.

关 键 词：Hardy–Littlewood–Sobolev inequality higher-order moments constraint concentration compactness principle almost optimal 

分 类 号：O178[理学—数学]