Hardy inequalities on metric measure spaces, III: The case q ≤ p ≤ 0 and applications
Kassymov A. Ruzhansky M. Suragan D.
25 January 2023Royal Society Publishing
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
2023#479Issue 2269
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 1q, respectively.
metric measure space , reverse Hardy inequality , reverse Hardy-Littlewood-Sobolev inequality , reverse Stein-Weiss inequality
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Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Gent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Department of Mathematics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Avenue, Nur-Sultan, 010000, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty, 050040, Kazakhstan
Department of Mathematics: Analysis Logic and Discrete Mathematics
School of Mathematical Sciences
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
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