Hardy inequalities on metric measure spaces

被引：17

作者：

Ruzhansky, Michael ^{[1
,2
,3
]}

Verma, Daulti ^{[1
,4
]}

机构：

[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[2] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

[3] Queen Mary Univ London, Sch Math Sci, London, England

[4] Univ Delhi, Miranda House Coll, Delhi 110007, India

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2019年 / 475卷 / 2223期

基金：

英国工程与自然科学研究理事会;

关键词：

Hardy inequalities; metric measure spaces; homogeneous group; hyperbolic space; Riemannian manifolds with negative curvature; SCALES;

D O I：

10.1098/rspa.2018.0310

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this note, we give several characterizations 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 R-n, on homogeneous groups, on hyperbolic spaces and on Cartan-Hadamard manifolds. We note that doubling conditions are not required for our analysis.

引用

页数：15

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