Hardy inequalities on metric measure spaces
File(s)Some Equivalence Conditions-2018-12-30-Proc-A.pdf (319.59 KB)
Accepted version
Author(s)
Ruzhansky, Michael
Verma, Daulti
Type
Journal Article
Abstract
In this note we give several characterisations of weights for two-weight
Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's
original inequality. We give examples obtaining new weighted Hardy inequalities on $\mathbb R^n$, on homogeneous groups, on hyperbolic spaces, and on Cartan-Hadamard manifolds. We note that doubling conditions are not required for our analysis.
Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's
original inequality. We give examples obtaining new weighted Hardy inequalities on $\mathbb R^n$, on homogeneous groups, on hyperbolic spaces, and on Cartan-Hadamard manifolds. We note that doubling conditions are not required for our analysis.
Date Issued
2019-03-01
Date Acceptance
2019-02-07
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 475 (2223)
ISSN
1364-5021
Publisher
Royal Society, The
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
475
Issue
2223
Copyright Statement
2019 The Author(s) Published by the Royal Society. All rights reserved.
Identifier
http://arxiv.org/abs/1806.03728v1
Subjects
math.FA
math.FA
math.AP
math.SP
26D10, 22E30
Notes
16 pages
Publication Status
Published
Date Publish Online
2019-03-06