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 inequal...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.展开更多
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)。
文摘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.
