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

A. Kassymov, Michael Ruzhansky (UGent) and D. Suragan
(2023) PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 479(2269).
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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<p≤q<∞ and p>q, respectively.
Keywords
General Physics and Astronomy, General Engineering, General Mathematics, Ghent Analysis & PDE center, 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

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MLA
Kassymov, A., et al. “Hardy Inequalities on Metric Measure Spaces, III : The Case Q<=p<0 and Applications.” PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 479, no. 2269, 2023, doi:10.1098/rspa.2022.0307.
APA
Kassymov, A., Ruzhansky, M., & Suragan, D. (2023). Hardy inequalities on metric measure spaces, III : the case q<=p<0 and applications. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 479(2269). https://doi.org/10.1098/rspa.2022.0307
Chicago author-date
Kassymov, A., Michael Ruzhansky, and D. Suragan. 2023. “Hardy Inequalities on Metric Measure Spaces, III : The Case Q<=p<0 and Applications.” PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 479 (2269). https://doi.org/10.1098/rspa.2022.0307.
Chicago author-date (all authors)
Kassymov, A., Michael Ruzhansky, and D. Suragan. 2023. “Hardy Inequalities on Metric Measure Spaces, III : The Case Q<=p<0 and Applications.” PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 479 (2269). doi:10.1098/rspa.2022.0307.
Vancouver
1.
Kassymov A, Ruzhansky M, Suragan D. Hardy inequalities on metric measure spaces, III : the case q<=p<0 and applications. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 2023;479(2269).
IEEE
[1]
A. Kassymov, M. Ruzhansky, and D. Suragan, “Hardy inequalities on metric measure spaces, III : the case q<=p<0 and applications,” PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 479, no. 2269, 2023.
@article{01H25SXNW77S9PG8VCN5P76XJR,
  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<p≤q<∞ and p>q, respectively.}},
  articleno    = {{20220307}},
  author       = {{Kassymov, A. and Ruzhansky, Michael and Suragan, D.}},
  issn         = {{1364-5021}},
  journal      = {{PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}},
  keywords     = {{General Physics and Astronomy,General Engineering,General Mathematics,Ghent Analysis & PDE center,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}},
  language     = {{eng}},
  number       = {{2269}},
  pages        = {{16}},
  title        = {{Hardy inequalities on metric measure spaces, III : the case q<=p<0 and applications}},
  url          = {{http://doi.org/10.1098/rspa.2022.0307}},
  volume       = {{479}},
  year         = {{2023}},
}
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