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

Aidyn Kassymov; Michael Ruzhansky; Durvudkhan Suragan

doi:10.1080/10652469.2019.1597080

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

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journal › Article

2 Citations (Scopus)

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 language	English
Journal	Integral Transforms and Special Functions
DOIs	https://doi.org/10.1080/10652469.2019.1597080
Publication status	Published - Jan 1 2019

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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

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

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Access to Document

10.1080/10652469.2019.1597080