Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups
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Abstract 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.
2007 ◽
Vol 2
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pp. 423-429
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2007 ◽
Vol 38
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pp. 437-454
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2017 ◽
Vol 29
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pp. 515-542
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2020 ◽
Vol 268
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pp. 5996-6032
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2004 ◽
Vol 134
(3)
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pp. 449-476
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