Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted Lp-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the L2-case.

Original languageEnglish
Article number56
JournalNonlinear Differential Equations and Applications
Volume24
Issue number5
DOIs
Publication statusPublished - Oct 1 2017
Externally publishedYes

Fingerprint

Lie groups
Sharp Constants
Hardy Inequality
Equivalence
Range of data

Keywords

  • Caffarelli–Kohn–Nirenberg inequality
  • Hardy inequality
  • Sobolev type inequality
  • Stratified Lie group

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups. / Ruzhansky, Michael; Suragan, Durvudkhan; Yessirkegenov, Nurgissa.

In: Nonlinear Differential Equations and Applications, Vol. 24, No. 5, 56, 01.10.2017.

Research output: Contribution to journalArticle

@article{4deaa2de70a941ed83f70c486e961d99,
title = "Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups",
abstract = "In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted Lp-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the L2-case.",
keywords = "Caffarelli–Kohn–Nirenberg inequality, Hardy inequality, Sobolev type inequality, Stratified Lie group",
author = "Michael Ruzhansky and Durvudkhan Suragan and Nurgissa Yessirkegenov",
year = "2017",
month = "10",
day = "1",
doi = "10.1007/s00030-017-0478-2",
language = "English",
volume = "24",
journal = "Nonlinear Differential Equations and Applications",
issn = "1021-9722",
publisher = "Birkhauser Verlag Basel",
number = "5",

}

TY - JOUR

T1 - Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

AU - Yessirkegenov, Nurgissa

PY - 2017/10/1

Y1 - 2017/10/1

N2 - In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted Lp-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the L2-case.

AB - In this short paper, we establish a range of Caffarelli–Kohn–Nirenberg and weighted Lp-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the L2-case.

KW - Caffarelli–Kohn–Nirenberg inequality

KW - Hardy inequality

KW - Sobolev type inequality

KW - Stratified Lie group

UR - http://www.scopus.com/inward/record.url?scp=85027988806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027988806&partnerID=8YFLogxK

U2 - 10.1007/s00030-017-0478-2

DO - 10.1007/s00030-017-0478-2

M3 - Article

VL - 24

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

IS - 5

M1 - 56

ER -