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 | |
| Publication status | Published - Dec 1 2017 |
Fingerprint
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
}
TY - JOUR
T1 - Anisotropic L 2 -weighted Hardy and L 2 -Caffarelli-Kohn-Nirenberg inequalities
AU - Ruzhansky, Michael
AU - Suragan, Durvudkhan
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
KW - Caffarelli-Kohn-Nirenberg inequality
KW - Hardy inequality
KW - homogeneous Lie group
KW - sharp remainder
KW - weighted inequalities
UR - http://www.scopus.com/inward/record.url?scp=85010866433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85010866433&partnerID=8YFLogxK
U2 - 10.1142/S0219199717500146
DO - 10.1142/S0219199717500146
M3 - Article
AN - SCOPUS:85010866433
VL - 19
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
SN - 0219-1997
IS - 6
M1 - 1750014
ER -