Hardy’s Identities and Inequalities on Cartan-Hadamard Manifolds

被引：0
|
作者：
Joshua Flynn
Nguyen Lam
Guozhen Lu
Saikat Mazumdar
机构：
[1] University of Connecticut,Department of Mathematics
[2] Grenfell Campus,School of Science & Environment
[3] Memorial University of Newfoundland,Department of Mathematics
[4] Indian Institute of Technology Bombay,undefined
来源：
The Journal of Geometric Analysis | 2023年 / 33卷
关键词：
Hardy’s identities; Hardy’s inequalities; Hardy-Poincaré–Sobolev inequalities; Cartan-Hadamard manifold; Hyperbolic space; 26D10; 46E35; 31C12; 53C21;
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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-Vázquez 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-Poincaré-Sobolev type inequalities on hyperbolic spaces in the literature.
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