Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journal › Article

Abstract

In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie groups.

Original languageEnglish
JournalIntegral Transforms and Special Functions
DOIs
Publication statusPublished - Jan 1 2019

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Homogeneous Groups
Lie groups
Norm

Keywords

  • 22E30
  • 43A80
  • fractional integral
  • fractional operator
  • Hardy–Littlewood–Sobolev inequality
  • homogeneous Lie group
  • Riesz potential
  • Stein–Weiss inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups. / Kassymov, Aidyn; Ruzhansky, Michael; Suragan, Durvudkhan.

In: Integral Transforms and Special Functions, 01.01.2019.

Research output: Contribution to journal › Article

Kassymov, A, Ruzhansky, M & Suragan, D 2019, 'Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups', Integral Transforms and Special Functions. https://doi.org/10.1080/10652469.2019.1597080
Kassymov A, Ruzhansky M, Suragan D. Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups. Integral Transforms and Special Functions. 2019 Jan 1. https://doi.org/10.1080/10652469.2019.1597080
Kassymov, Aidyn ; Ruzhansky, Michael ; Suragan, Durvudkhan. / Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups. In: Integral Transforms and Special Functions. 2019.
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