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.
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The authors were supported in parts by the EPSRC Grant EP/R003025/1 and by the Leverhulme Grant RPG-2017-151, as well as by the MESRK Grant 5127/GF4. The second author was also supported by the Ministry of Science of the Russian Federation (the Agreement No. 02.a03.21.0008). The third author was supported by the MESRK Grant 0825/GF4. No new data was collected or generated during the course of research.
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Ruzhansky, M., Suragan, D. & Yessirkegenov, N. Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups. Nonlinear Differ. Equ. Appl. 24, 56 (2017). https://doi.org/10.1007/s00030-017-0478-2
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DOI: https://doi.org/10.1007/s00030-017-0478-2