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Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups
Semigroup Forum ( IF 0.7 ) Pub Date : 2020-06-10 , DOI: 10.1007/s00233-020-10110-9
Michael Ruzhansky , Durvudkhan Suragan , Nurgissa Yessirkegenov

In this paper we describe the Euler semigroup $$\{e^{-t\mathbb {E}^{*}\mathbb {E}}\}_{t>0}$$ { e - t E ∗ E } t > 0 on homogeneous Lie groups, which allows us to obtain various types of the Hardy–Sobolev and Gagliardo–Nirenberg type inequalities for the Euler operator $$\mathbb {E}$$ E . Moreover, the sharp remainder terms of the Sobolev type inequality, maximal Hardy inequality and $$|\cdot |$$ | · | -radial weighted Hardy–Sobolev type inequality are established.

中文翻译:

齐次群上的欧拉半群、Hardy-Sobolev 和 Gagliardo-Nirenberg 型不等式

在本文中,我们描述了欧拉半群 $$\{e^{-t\mathbb {E}^{*}\mathbb {E}}\}_{t>0}$$ { e - t E ∗ E } t > 0 在齐次李群上,这使我们能够获得欧拉算子 $$\mathbb {E}$$ E 的各种类型的 Hardy-Sobolev 和 Gagliardo-Nirenberg 型不等式。此外,Sobolev 型不等式、极大哈代不等式和 $$|\cdot |$$ | 的锐余项 · | -径向加权Hardy-Sobolev型不等式成立。
更新日期:2020-06-10
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