Hardy inequalities on metric measure spaces, III: the case q ≤ p ≤ 0 and applications

被引：2

作者：

Kassymov, A. ^{[1
,4
,5
]}

Ruzhansky, M. ^{[1
,2
]}

Suragan, D. ^{[3
]}

机构：

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

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

[3] Nazarbayev Univ, Sch Sci & Technol, Dept Math, 53 Kabanbay Batyr Ave, Nur Sultan 010000, Kazakhstan

[4] Inst Math & Math Modeling, 125 Pushkin St, Alma Ata 050010, Kazakhstan

[5] Al Farabi Kazakh Natl Univ, 71 Al-Farabi Ave, Alma Ata 050040, Kazakhstan

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2023年 / 479卷 / 2269期

基金：

英国工程与自然科学研究理事会;

关键词：

reverse Hardy inequality; metric measure space; reverse Hardy-Littlewood-Sobolev inequality; reverse Stein-Weiss inequality; STEIN-WEISS INEQUALITIES; LITTLEWOOD-SOBOLEV; FRACTIONAL INTEGRALS; SHARP CONSTANTS; EXISTENCE;

D O I：

10.1098/rspa.2022.0307

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 paper, we obtain a reverse version of the integral Hardy inequality on metric measure space with two negative exponents. For applications we show the reverse Hardy-Littlewood-Sobolev and the Stein-Weiss inequalities with two negative exponents on homogeneous Lie groups and with arbitrary quasi-norm, the result of which appears to be new in the Euclidean space. This work further complements the ranges of p and q (namely, q <= p<0) considered in the work of Ruzhansky & Verma (Ruzhansky & Verma 2019 Proc. R. Soc. A 475, 20180310 (); Ruzhansky & Verma. 2021 Proc. R. Soc. A 477, 20210136 ()), which treated the cases 1<p <= qq, respectively.

引用

页数：16

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