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Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups

  • Michael RuzhanskyEmail author
  • Durvudkhan Suragan
  • Nurgissa Yessirkegenov
Open Access
Article

Abstract

In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted \(L^{p}\)-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the \(L^{2}\)-case.

Keywords

Sobolev type inequality Hardy inequality Caffarelli–Kohn–Nirenberg inequality Stratified Lie group 

Mathematics Subject Classification

22E30 43A80 

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Institute of Mathematics and Mathematical ModellingAlmatyKazakhstan
  3. 3.RUDN UniversityMoscowRussia

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