Options
Hardy’s Identities and Inequalities on Cartan-Hadamard Manifolds
Journal
Journal of Geometric Analysis
ISSN
10506926
Date Issued
2023-01-01
Author(s)
Flynn, Joshua
Lam, Nguyen
Lu, Guozhen
Mazumdar, Saikat
Abstract
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.
Subjects