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

Michael Ruzhansky, Durvudkhan Suragan

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16 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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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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