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

Michael Ruzhansky; Durvudkhan Suragan

doi:10.1142/S0219199717500146

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

Michael Ruzhansky, Durvudkhan Suragan

Department of Mathematics

Research output: Contribution to journal › Article

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 language	English
Article number	1750014
Journal	Communications in Contemporary Mathematics
Volume	19
Issue number	6
DOIs	https://doi.org/10.1142/S0219199717500146
Publication status	Published - 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

Cite this

Ruzhansky, M., & Suragan, D. (2017). Anisotropic L ² -weighted Hardy and L ² -Caffarelli-Kohn-Nirenberg inequalities. Communications in Contemporary Mathematics, 19(6), [1750014]. https://doi.org/10.1142/S0219199717500146

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10.1142/S0219199717500146