Journal
FORUM MATHEMATICUM
Volume 34, Issue 5, Pages 1147-1158Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/forum-2021-0110
Keywords
Riesz potential; fractional operator; reverse Hardy-Littlewood-Sobolev inequality; reverse Stein-Weiss inequality; reverse Hardy inequality; reverse Sobolev inequality; reverse Caffarelli-Kohn-Nirenberg inequality; homogeneous Lie group
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Funding
- Science Committee of the MES RK [AP09258745]
- FWO Odysseus Project [G.0H94.18N]
- Methusalem programme of the Ghent University Special Research Fund (BOF) [01M01021]
- EPSRC [EP/R003025/1]
- Nazarbayev University Program [091019CRP2120]
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In this note, we prove the reverse Stein-Weiss inequality on general homogeneous Lie groups, extending previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play crucial roles in our proofs. Additionally, we demonstrate reverse Hardy, Hardy-Littlewood-Sobolev, L-p-Sobolev, and L-p-Caffarelli-Kohn-Nirenberg inequalities on homogeneous Lie groups.
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.
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