Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, generalised weighted (Formula presented.)-Hardy, (Formula presented.)-Caffarelli–Kohn–Nirenberg, and (Formula presented.)-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted (Formula presented.)-Rellich type inequality with the boundary term is obtained.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalRevista Matematica Complutense
DOIs
Publication statusAccepted/In press - Jun 29 2018

Fingerprint

Term
Hardy-type Inequality
Uncertainty Principle

Keywords

  • Boundary term
  • Caffarelli–Kohn–Nirenberg inequality
  • Hardy inequality
  • Rellich inequality
  • Stratified Lie group
  • Uncertainty principle

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups. / Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan.

In: Revista Matematica Complutense, 29.06.2018, p. 1-17.

Research output: Contribution to journalArticle

@article{6d3fa1a6989f41f582444bdfcf3c5890,
title = "Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups",
abstract = "In this paper, generalised weighted (Formula presented.)-Hardy, (Formula presented.)-Caffarelli–Kohn–Nirenberg, and (Formula presented.)-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted (Formula presented.)-Rellich type inequality with the boundary term is obtained.",
keywords = "Boundary term, Caffarelli–Kohn–Nirenberg inequality, Hardy inequality, Rellich inequality, Stratified Lie group, Uncertainty principle",
author = "Michael Ruzhansky and Bolys Sabitbek and Durvudkhan Suragan",
year = "2018",
month = "6",
day = "29",
doi = "10.1007/s13163-018-0268-3",
language = "English",
pages = "1--17",
journal = "Revista Matematica Complutense",
issn = "1139-1138",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups

AU - Ruzhansky, Michael

AU - Sabitbek, Bolys

AU - Suragan, Durvudkhan

PY - 2018/6/29

Y1 - 2018/6/29

N2 - In this paper, generalised weighted (Formula presented.)-Hardy, (Formula presented.)-Caffarelli–Kohn–Nirenberg, and (Formula presented.)-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted (Formula presented.)-Rellich type inequality with the boundary term is obtained.

AB - In this paper, generalised weighted (Formula presented.)-Hardy, (Formula presented.)-Caffarelli–Kohn–Nirenberg, and (Formula presented.)-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted (Formula presented.)-Rellich type inequality with the boundary term is obtained.

KW - Boundary term

KW - Caffarelli–Kohn–Nirenberg inequality

KW - Hardy inequality

KW - Rellich inequality

KW - Stratified Lie group

KW - Uncertainty principle

UR - http://www.scopus.com/inward/record.url?scp=85049146920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049146920&partnerID=8YFLogxK

U2 - 10.1007/s13163-018-0268-3

DO - 10.1007/s13163-018-0268-3

M3 - Article

SP - 1

EP - 17

JO - Revista Matematica Complutense

JF - Revista Matematica Complutense

SN - 1139-1138

ER -