Hardy inequalities on metric measure spaces, IV: The case p=1

被引：0

作者：

Ruzhansky, Michael ^{[2
,3
]}

Shriwastawa, Anjali ^{[1
]}

Tiwari, Bankteshwar ^{[1
]}

机构：

[1] Banaras Hindu Univ, DST Ctr Interdisciplinary Math Sci, Varanasi 221005, India

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

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

来源：

FORUM MATHEMATICUM | 2024年 / 36卷 / 06期

关键词：

Integral Hardy inequalities; homogeneous Lie groups; metric measure spaces; quasi-norm; Riemannian manifold with negative curvature; hyperbolic spaces; SCALES;

D O I：

10.1515/forum-2023-0319

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p=1 and 1 <= q<infinity. This result complements the Hardy inequalities obtained in [M. Ruzhansky and D. Verma, Hardy inequalities on metric measure spaces, Proc. Roy. Soc. A. 475 2019, 2223, Article ID 20180310] in the case 1<p <= q<infinity . The case p=1 requires a different argument and does not follow as the limit of known inequalities for p>1 . As a byproduct, we also obtain the best constant in the established inequality. We give examples obtaining new weighted Hardy inequalities on homogeneous Lie groups, on hyperbolic spaces and on Cartan-Hadamard manifolds for the case p=1 and 1 <= q<infinity.

引用

页码：1603 / 1611

页数：9

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