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Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems

Aidyn Kassymov (UGent) , Michael Ruzhansky (UGent) and Durvudkhan Suragan
(2022) POTENTIAL ANALYSIS. 59(4). p.1971-1994
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Abstract
In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyapunov-type inequality for the Riesz potential on homogeneous Lie groups. The obtained Lyapunov inequality for the Riesz potential is new already in the classical setting of R-N. As an application, we give two-sided estimate for the first eigenvalue of the Riesz potential. Also, we obtain Lyapunov inequality for the system of the fractional p-sub-Laplacian equations and give an application to estimate its eigenvalues.
Keywords
Ghent Analysis & PDE center, Fractional Gagliardo-Nirenberg inequality, Fractional Caffarelli-Kohn-Nirenberg inequality, Fractional Lyapunov-type inequality, Homogeneous Lie group, HARDY, RELLICH

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MLA
Kassymov, Aidyn, et al. “Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-Type Inequalities, and Applications to Riesz Potentials and p-Sub-Laplacian Systems.” POTENTIAL ANALYSIS, vol. 59, no. 4, 2022, pp. 1971–94, doi:10.1007/s11118-022-10029-6.
APA
Kassymov, A., Ruzhansky, M., & Suragan, D. (2022). Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems. POTENTIAL ANALYSIS, 59(4), 1971–1994. https://doi.org/10.1007/s11118-022-10029-6
Chicago author-date
Kassymov, Aidyn, Michael Ruzhansky, and Durvudkhan Suragan. 2022. “Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-Type Inequalities, and Applications to Riesz Potentials and p-Sub-Laplacian Systems.” POTENTIAL ANALYSIS 59 (4): 1971–94. https://doi.org/10.1007/s11118-022-10029-6.
Chicago author-date (all authors)
Kassymov, Aidyn, Michael Ruzhansky, and Durvudkhan Suragan. 2022. “Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-Type Inequalities, and Applications to Riesz Potentials and p-Sub-Laplacian Systems.” POTENTIAL ANALYSIS 59 (4): 1971–1994. doi:10.1007/s11118-022-10029-6.
Vancouver
1.
Kassymov A, Ruzhansky M, Suragan D. Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems. POTENTIAL ANALYSIS. 2022;59(4):1971–94.
IEEE
[1]
A. Kassymov, M. Ruzhansky, and D. Suragan, “Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems,” POTENTIAL ANALYSIS, vol. 59, no. 4, pp. 1971–1994, 2022.
@article{01HP4PKBQD2D986ETNJQ41ZPRB,
  abstract     = {{In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyapunov-type inequality for the Riesz potential on homogeneous Lie groups. The obtained Lyapunov inequality for the Riesz potential is new already in the classical setting of R-N. As an application, we give two-sided estimate for the first eigenvalue of the Riesz potential. Also, we obtain Lyapunov inequality for the system of the fractional p-sub-Laplacian equations and give an application to estimate its eigenvalues.}},
  author       = {{Kassymov, Aidyn and Ruzhansky, Michael and Suragan, Durvudkhan}},
  issn         = {{0926-2601}},
  journal      = {{POTENTIAL ANALYSIS}},
  keywords     = {{Ghent Analysis & PDE center,Fractional Gagliardo-Nirenberg inequality,Fractional Caffarelli-Kohn-Nirenberg inequality,Fractional Lyapunov-type inequality,Homogeneous Lie group,HARDY,RELLICH}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1971--1994}},
  title        = {{Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems}},
  url          = {{http://doi.org/10.1007/s11118-022-10029-6}},
  volume       = {{59}},
  year         = {{2022}},
}
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