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 <= q<infinity and p>q, respectively.
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页数：16
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