Lp-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups
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Published version
Author(s)
Ozawa, Tohru
Ruzhansky, Michael
Suragan, Durvudkhan
Type
Journal Article
Abstract
We prove $L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous
groups, which is one of most general subclasses of nilpotent Lie groups, all
with sharp constants. We also discuss some of their consequences. Already in
the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view
of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.
groups, which is one of most general subclasses of nilpotent Lie groups, all
with sharp constants. We also discuss some of their consequences. Already in
the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view
of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.
Date Issued
2019-03
Date Acceptance
2018-07-02
Citation
Quarterly Journal of Mathematics, 2019, 70 (1), pp.305-318
ISSN
0033-5606
Publisher
Oxford University Press (OUP)
Start Page
305
End Page
318
Journal / Book Title
Quarterly Journal of Mathematics
Volume
70
Issue
1
Copyright Statement
© The Author(s) 2018. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Identifier
http://arxiv.org/abs/1605.02520v2
Grant Number
RPG-2014-002
EP/K039407/1
EP/R003025/1
RPG-2017-151
Subjects
math.FA
math.FA
math.AP
22E30, 43A80
Notes
12 pages; a revised version. arXiv admin note: text overlap with arXiv:1603.06239
Publication Status
Published
Date Publish Online
2018-10-04