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arXiv · 2007.00516

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

Aidyn Kassymov·Michael Ruzhansky·Niyaz Tokmagambetov·Berikbol T. Torebek
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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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Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov, Berikbol T. Torebek. 2020-07-01. Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives. https://doi.org/10.1007/s43037-020-00097-4

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