On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups

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Title: On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups
Author(s): Ruzhansky, M
Suragan, D
Item Type: Journal Article
Abstract: In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale-Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also show a family of Poincar\'e inequalities as well as inequalities involving the weighted and unweighted $p$-sub-Laplacians.
Publication Date: 10-Nov-2016
Date of Acceptance: 24-Oct-2016
URI: http://hdl.handle.net/10044/1/42271
DOI: https://dx.doi.org/10.1016/j.jde.2016.10.028
ISSN: 1090-2732
Publisher: Elsevier
Start Page: 1799
End Page: 1821
Journal / Book Title: Journal of Differential Equations
Volume: 262
Issue: 3
Copyright Statement: © 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: math.FA
math.FA
math.AP
22E30, 43A80
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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