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

Результат исследований › рецензирование

4 Цитирования (Scopus)

Аннотация

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.

Язык оригинала	English
Страницы (с-по)	1147-1158
Число страниц	12
Журнал	Forum Mathematicum
Том	34
Номер выпуска	5
DOI	https://doi.org/10.1515/forum-2021-0110
Состояние	Published - сент. 1 2022

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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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.",

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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.

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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.

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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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