Anisotropic L2-weighted hardy and L2-Caffarelli-Kohn-Nirenberg inequalities
File(s)RS_L2-CKN-2016-10-29.pdf (283.86 KB) s0219199717500146.pdf (178.05 KB)
Accepted version
Published version
Author(s)
Ruzhansky, M
Suragan, D
Type
Journal Article
Abstract
We establish sharp remainder terms of the
L
2
-Ca arelli-Kohn-Niren-
berg inequalities on homogeneous groups, yielding the inequalities with best con-
stants. Our methods also give new sharp Ca arelli-Kohn-Nirenberg type inequali-
ties in
R
n
with arbitrary quasi-norms. We also present explicit examples to illustrate
our results for di erent weights and in abelian cases.
L
2
-Ca arelli-Kohn-Niren-
berg inequalities on homogeneous groups, yielding the inequalities with best con-
stants. Our methods also give new sharp Ca arelli-Kohn-Nirenberg type inequali-
ties in
R
n
with arbitrary quasi-norms. We also present explicit examples to illustrate
our results for di erent weights and in abelian cases.
Date Issued
2017-01-25
Date Acceptance
2016-10-21
Citation
Communications in Contemporary Mathematics, 2017, 19 (6)
ISSN
1793-6683
Publisher
World Scientific Publishing
Journal / Book Title
Communications in Contemporary Mathematics
Volume
19
Issue
6
Copyright Statement
© The Author(s)
This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Grant Number
EP/K039407/1
RPG-2014-002
Subjects
math.FA
math.AP
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Article Number
1750014