Author:
Ruzhansky Michael,Suragan Durvudkhan,Yessirkegenov Nurgissa
Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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