Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups

2018/05/04 by Ruzhansky, Michael, Suragan, Durvudkhan, Yessirkegenov, Nurgissa
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.01842

Abstract

In this paper we describe the Euler semigroup \e^-t𝔼^*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 𝔼. Moreover, the sharp remainder terms of the Sobolev type inequality, maximal Hardy inequality and |⋅|-radial weighted Hardy-Sobolev type inequality are established.

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