
Some weak geometric inequalities for the Riesz potential
- Author
- Aidyn Kassymov (UGent)
- Organization
- 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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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8714797
- 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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