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Eurasian Mathematical Journal, 2020, Volume 11, Number 3, Pages 42–50
DOI: https://doi.org/10.32523/2077-9879-2020-11-3-42-50 (Mi emj373) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Some weak geometric inequalities for the Riesz potential

A. Kassymovabc

a Al-Farabi Kazakh National University, 71 Al-Farabi Ave, 050040 Almaty, Kazakhstan
b Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, S8 Building, Ghent, Belgium
c Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2020-11-3-42-50
Abstract: In the present paper, we prove that the first eigenvalue of the Riesz potential is weakly maximised in a quasi-ball among all Haar measurable sets on homogeneous Lie groups. It is an analogue of the classical Rayleigh–Faber–Krahn inequality for the Riesz potential. We also prove a weak version of the Hong–Krahn–Szegö inequality for the Riesz potential on homogeneous Lie groups.
Keywords and phrases: convolution operators, Riesz potential, Rayleigh–Faber–Krahn inequality, Hong–Krahn–Szegö inequality, homogeneous Lie group.
Funding agency Grant number
Fonds Wetenschappelijk Onderzoek G.0H94.18N
Ministry of Education and Science of the Republic of Kazakhstan AP05130981
The author was partially supported by the Fonds Wetenschappelijk Onderzoek (FWO) Odysseus 1, grant G.0H94.18N: Analysis and Partial Differential Equations, and by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan, grant AP05130981.
Received: 18.06.2019
Bibliographic databases:
Document Type: Article
MSC: 35P99, 47G40
Language: English
Citation: A. Kassymov, “Some weak geometric inequalities for the Riesz potential”, Eurasian Math. J., 11:3 (2020), 42–50
Citation in format AMSBIB
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\by A.~Kassymov
\paper Some weak geometric inequalities for the Riesz potential
\jour Eurasian Math. J.
\yr 2020
\vol 11
\issue 3
\pages 42--50
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