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

In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted Lp-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 L2-case. © 2017, The Author(s).

Authors
Ruzhansky M.1 , Suragan D. 2, 3 , Yessirkegenov N.1, 2
Journal
Nonlinear Differential Equations and Applications
Publisher
Birkhauser Verlag AG
Number of issue
5
Language
English
Status
Published
Link
External link
DOI
10.1007/S00030-017-0478-2
Number
56
Volume
24
Year
2017
Organizations
  • 1 Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
  • 2 Institute of Mathematics and Mathematical Modelling, 125 Pushkin str., Almaty, 050010, Kazakhstan
  • 3 RUDN University, 6 Miklukho-Maklay str., Moscow, 117198, Russian Federation
Keywords
Caffarelli–Kohn–Nirenberg inequality; Hardy inequality; Sobolev type inequality; Stratified Lie group
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