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 |
|---|---|
| Pages (from-to) | 643-655 |
| Number of pages | 13 |
| Journal | Integral Transforms and Special Functions |
| Volume | 30 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Jan 1 2019 |
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
Fingerprint Dive into the research topics of 'Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups'. Together they form a unique fingerprint.
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, 30(8), 643-655. https://doi.org/10.1080/10652469.2019.1597080