Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for some fractional derivatives,Banach Journal of Mathematical Analysis

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Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for some fractional derivatives
Banach Journal of Mathematical Analysis ( IF 1.2 ) Pub Date : 2020-10-07 , DOI: 10.1007/s43037-020-00097-4
Aidyn Kassymov , Michael Ruzhansky , Niyaz Tokmagambetov , Berikbol T. Torebek

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.

中文翻译：

一些分数阶导数的 Sobolev、Hardy、Gagliardo-Nirenberg 和 Caffarelli-Kohn-Nirenberg 型不等式

在本文中，我们展示了分数阶微分算子的不同不等式。特别是，获得了 Caputo、Riemann-Liouville 和 Hadamard 导数的 Sobolev、Hardy、Gagliardo-Nirenberg 和 Caffarelli-Kohn-Nirenberg 型不等式。此外，我们展示了这些不等式的一些应用。

更新日期：2020-10-07

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