Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups

Aidyn Kassymov; Michael Ruzhansky; Durvudkhan Suragan

doi:10.1515/forum-2021-0110

Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this note, we prove the reverse Stein–Weiss inequality on general homogeneous Lie groups. The results obtained extend previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play key roles in our proofs. Also, we prove reverse Hardy, Hardy–Littlewood–Sobolev, Lp-Sobolev and L^p-Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.

Original language	English
Pages (from-to)	1147-1158
Number of pages	12
Journal	Forum Mathematicum
Volume	34
Issue number	5
DOIs	https://doi.org/10.1515/forum-2021-0110
Publication status	Published - Sept 1 2022

Keywords

fractional operator
Homogeneous Lie group
reverse Caffarelli–Kohn–Nirenberg inequality
reverse Hardy inequality
reverse Hardy–Littlewood–Sobolev inequality
reverse Sobolev inequality
reverse Stein–Weiss inequality
Riesz potential

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/forum-2021-0110

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title = "Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups",

abstract = "In this note, we prove the reverse Stein–Weiss inequality on general homogeneous Lie groups. The results obtained extend previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play key roles in our proofs. Also, we prove reverse Hardy, Hardy–Littlewood–Sobolev, Lp-Sobolev and Lp-Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.",

keywords = "fractional operator, Homogeneous Lie group, reverse Caffarelli–Kohn–Nirenberg inequality, reverse Hardy inequality, reverse Hardy–Littlewood–Sobolev inequality, reverse Sobolev inequality, reverse Stein–Weiss inequality, Riesz potential",

author = "Aidyn Kassymov and Michael Ruzhansky and Durvudkhan Suragan",

note = "Funding Information: The authors were also supported in parts by Science Committee of the MES RK (Grant number AP09258745), Nazarbayev University Program 091019CRP2120, the FWO Odysseus Project G.0H94.18N, and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021), and EPSRC Grant EP/R003025/1. Publisher Copyright: {\textcopyright} 2022 De Gruyter. All rights reserved.",

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AU - Kassymov, Aidyn

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

N1 - Funding Information: The authors were also supported in parts by Science Committee of the MES RK (Grant number AP09258745), Nazarbayev University Program 091019CRP2120, the FWO Odysseus Project G.0H94.18N, and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021), and EPSRC Grant EP/R003025/1. Publisher Copyright: © 2022 De Gruyter. All rights reserved.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - In this note, we prove the reverse Stein–Weiss inequality on general homogeneous Lie groups. The results obtained extend previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play key roles in our proofs. Also, we prove reverse Hardy, Hardy–Littlewood–Sobolev, Lp-Sobolev and Lp-Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.

AB - In this note, we prove the reverse Stein–Weiss inequality on general homogeneous Lie groups. The results obtained extend previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play key roles in our proofs. Also, we prove reverse Hardy, Hardy–Littlewood–Sobolev, Lp-Sobolev and Lp-Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.

KW - fractional operator

KW - Homogeneous Lie group

KW - reverse Caffarelli–Kohn–Nirenberg inequality

KW - reverse Hardy inequality

KW - reverse Hardy–Littlewood–Sobolev inequality

KW - reverse Sobolev inequality

KW - reverse Stein–Weiss inequality

KW - Riesz potential

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U2 - 10.1515/forum-2021-0110

DO - 10.1515/forum-2021-0110

M3 - Article

AN - SCOPUS:85135086870

SN - 0933-7741

VL - 34

SP - 1147

EP - 1158

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 5

ER -

Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups

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Keywords

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