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Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives

Aidyn Kassymov (UGent) , Michael Ruzhansky (UGent) , Niyaz Tokmagambetov (UGent) and Berikbol Torebek (UGent)
(2021) BANACH JOURNAL OF MATHEMATICAL ANALYSIS. 15.
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Abstract
In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for the Caputo, Riemann-Liouville and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities.

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MLA
Kassymov, Aidyn, et al. “Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg Type  Inequalities for Some Fractional Derivatives.” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 15, 2021, doi:10.1007/s43037-020-00097-4.
APA
Kassymov, A., Ruzhansky, M., Tokmagambetov, N., & Torebek, B. (2021). Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type  inequalities for some fractional derivatives. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 15. https://doi.org/10.1007/s43037-020-00097-4
Chicago author-date
Kassymov, Aidyn, Michael Ruzhansky, Niyaz Tokmagambetov, and Berikbol Torebek. 2021. “Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg Type  Inequalities for Some Fractional Derivatives.” BANACH JOURNAL OF MATHEMATICAL ANALYSIS 15. https://doi.org/10.1007/s43037-020-00097-4.
Chicago author-date (all authors)
Kassymov, Aidyn, Michael Ruzhansky, Niyaz Tokmagambetov, and Berikbol Torebek. 2021. “Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg Type  Inequalities for Some Fractional Derivatives.” BANACH JOURNAL OF MATHEMATICAL ANALYSIS 15. doi:10.1007/s43037-020-00097-4.
Vancouver
1.
Kassymov A, Ruzhansky M, Tokmagambetov N, Torebek B. Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type  inequalities for some fractional derivatives. BANACH JOURNAL OF MATHEMATICAL ANALYSIS. 2021;15.
IEEE
[1]
A. Kassymov, M. Ruzhansky, N. Tokmagambetov, and B. Torebek, “Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type  inequalities for some fractional derivatives,” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 15, 2021.
@article{8688353,
  abstract     = {{In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for the Caputo, Riemann-Liouville and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities.}},
  articleno    = {{6}},
  author       = {{Kassymov, Aidyn and Ruzhansky, Michael and Tokmagambetov, Niyaz and Torebek, Berikbol}},
  issn         = {{2662-2033}},
  journal      = {{BANACH JOURNAL OF MATHEMATICAL ANALYSIS}},
  language     = {{eng}},
  pages        = {{24}},
  title        = {{Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type  inequalities for some fractional derivatives}},
  url          = {{http://dx.doi.org/10.1007/s43037-020-00097-4}},
  volume       = {{15}},
  year         = {{2021}},
}
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