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

  • Aidyn Kassymov EMAIL logo , Michael Ruzhansky and Durvudkhan Suragan ORCID logo
Published/Copyright: July 23, 2022

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, L p -Sobolev and L p -Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.

MSC 2010: 22E30; 43A80

Communicated by Jan Frahm


Award Identifier / Grant number: AP09258745

Award Identifier / Grant number: 091019CRP2120

Award Identifier / Grant number: EP/R003025/1

Funding statement: 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.

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Received: 2021-05-04
Revised: 2022-01-28
Published Online: 2022-07-23
Published in Print: 2022-09-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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