Hardy inequalities on metric measure spaces, III: the case q ≤ p ≤ 0 and applications-Reference-Cited by-同舟云学术

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

Published:2023-01 Issue:2269 Volume:479 Page:
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Kassymov A.¹²³,Ruzhansky M.¹⁴^ORCID,Suragan D.⁵

Affiliation:

1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Gent, Belgium

2. Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty 050010, Kazakhstan

3. Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty 050040, Kazakhstan

4. School of Mathematical Sciences, Queen Mary University of London, London, UK

5. Department of Mathematics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Avenue, Nur-Sultan 010000, Kazakhstan

Abstract

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 ( doi:10.1098/rspa.2018.0310 ); Ruzhansky & Verma. 2021 Proc. R. Soc. A 477 , 20210136 ( doi:10.1098/rspa.2021.0136 )), which treated the cases 1 q , respectively.

Funder

Fonds Wetenschappelijk Onderzoek

Universiteit Gent

Ministry of Education and Science of the Republic of Kazakhstan

Engineering and Physical Sciences Research Council

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2022.0307

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