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Some weak geometric inequalities for the Riesz potential

Aidyn Kassymov (UGent)
(2020) EURASIAN MATHEMATICAL JOURNAL. 11(3). p.42-50
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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-Szego inequality for the Riesz potential on homogeneous Lie groups.
Keywords
ISOPERIMETRIC-INEQUALITIES, convolution operators, Riesz potential, Rayleigh-Faber-Krahn inequality, Hong-KrahnSzego inequality, homogeneous Lie group

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MLA
Kassymov, Aidyn. “Some Weak Geometric Inequalities for the Riesz Potential.” EURASIAN MATHEMATICAL JOURNAL, vol. 11, no. 3, 2020, pp. 42–50, doi:10.32523/2077-9879-2020-11-3-42-50.
APA
Kassymov, A. (2020). Some weak geometric inequalities for the Riesz potential. EURASIAN MATHEMATICAL JOURNAL, 11(3), 42–50. https://doi.org/10.32523/2077-9879-2020-11-3-42-50
Chicago author-date
Kassymov, Aidyn. 2020. “Some Weak Geometric Inequalities for the Riesz Potential.” EURASIAN MATHEMATICAL JOURNAL 11 (3): 42–50. https://doi.org/10.32523/2077-9879-2020-11-3-42-50.
Chicago author-date (all authors)
Kassymov, Aidyn. 2020. “Some Weak Geometric Inequalities for the Riesz Potential.” EURASIAN MATHEMATICAL JOURNAL 11 (3): 42–50. doi:10.32523/2077-9879-2020-11-3-42-50.
Vancouver
1.
Kassymov A. Some weak geometric inequalities for the Riesz potential. EURASIAN MATHEMATICAL JOURNAL. 2020;11(3):42–50.
IEEE
[1]
A. Kassymov, “Some weak geometric inequalities for the Riesz potential,” EURASIAN MATHEMATICAL JOURNAL, vol. 11, no. 3, pp. 42–50, 2020.
@article{8714797,
  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-Szego inequality for the Riesz potential on homogeneous Lie groups.}},
  author       = {{Kassymov, Aidyn}},
  issn         = {{2077-9879}},
  journal      = {{EURASIAN MATHEMATICAL JOURNAL}},
  keywords     = {{ISOPERIMETRIC-INEQUALITIES,convolution operators,Riesz potential,Rayleigh-Faber-Krahn inequality,Hong-KrahnSzego inequality,homogeneous Lie group}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{42--50}},
  title        = {{Some weak geometric inequalities for the Riesz potential}},
  url          = {{http://dx.doi.org/10.32523/2077-9879-2020-11-3-42-50}},
  volume       = {{11}},
  year         = {{2020}},
}
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