Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities

Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journal › Article

13 Citations (Scopus)

Abstract

We establish sharp remainder terms of the L2-Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg-type inequalities in ?n with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.

Original languageEnglish
Article number1750014
JournalCommunications in Contemporary Mathematics
Volume19
Issue number6
DOIs
Publication statusPublished - Dec 1 2017

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Caffarelli-Kohn-Nirenberg Inequalities
Homogeneous Groups
Best Constants
Error term
Norm
Arbitrary

Keywords

  • Caffarelli-Kohn-Nirenberg inequality
  • Hardy inequality
  • homogeneous Lie group
  • sharp remainder
  • weighted inequalities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities. / Ruzhansky, Michael; Suragan, Durvudkhan.

In: Communications in Contemporary Mathematics, Vol. 19, No. 6, 1750014, 01.12.2017.

Research output: Contribution to journal › Article

Ruzhansky, M & Suragan, D 2017, 'Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities', Communications in Contemporary Mathematics, vol. 19, no. 6, 1750014. https://doi.org/10.1142/S0219199717500146
Ruzhansky M, Suragan D. Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities. Communications in Contemporary Mathematics. 2017 Dec 1;19(6). 1750014. https://doi.org/10.1142/S0219199717500146
Ruzhansky, Michael ; Suragan, Durvudkhan. / Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities. In: Communications in Contemporary Mathematics. 2017 ; Vol. 19, No. 6.
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