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

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


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.


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

Mathematics Subject Classification

22E30 43A80 


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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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