Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds

被引：8

作者：

Flynn, Joshua ^{[1
]}

Lam, Nguyen ^{[2
]}

Lu, Guozhen ^{[1
]}

Mazumdar, Saikat ^{[3
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Mem Univ Newfoundland, Sch Sci & Environm, Grenfell Campus, Corner Brook, NL A2H 5G4, Canada

[3] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 01期

关键词：

Hardy's identities; Hardy's inequalities; Hardy-Poincare-Sobolev inequalities; Cartan-Hadamard manifold; Hyperbolic space; POINCARE INEQUALITIES; RELLICH INEQUALITIES; OPTIMAL CONSTANTS; SPACES; SCHRODINGER; OPERATOR;

D O I：

10.1007/s12220-022-01079-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy inequalities. These Hardy inequalities are in the spirit of Brezis-Vazquez in the Euclidean spaces. As direct consequences, we establish several Hardy type inequalities that provide substantial improvements as well as simple understandings to many known Hardy inequalities and Hardy-Poincare-Sobolev type inequalities on hyperbolic spaces in the literature.

引用

页数：34

共 52 条

[1] An improved Hardy-Sobolev inequality and its application [J].