Cartan-Hadamard流形上关于Lorentz范数的Trudinger-Moser不等式  

TRUDINGER-MOSER INEQUALITIES ON CARTAN-HADAMARD MANIFOLDS UNDER LORENTZ NORMS

作　　者：张佳杰 ZHANG Jia-jie(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2024年第4期283-292,共10页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12071353)。

摘　　要：本文研究了Cartan-Hadamard流形上带Lorentz范数的Trudinger-Moser不等式.利用了相关格林函数的逐点估计以及O’Neil不等式,我们得到了该不等式的最佳常数,推广了相应欧氏空间上的结果.The aim of this paper is to study Trudinger-Moser inequalities on a Cartan-Hadamard manifold with Lorentz norm.By using the pointwise estimates of Green’s function and O’Neil inequality,we obtain the sharp constants of such inequalities,which generalize the corre-sponding results in Euclidean spaces.

关 键 词：Trudinger-Moser不等式 LORENTZ空间 RIEMANNIAN流形 负曲率 最佳常数 

分 类 号：O177[理学—数学]