Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups
Kassymov A. Ruzhansky M. Suragan D.
1 September 2022De Gruyter Open Ltd
Forum Mathematicum
2022#34Issue 51147 - 1158 pp.
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, Lp-Sobolev and Lp-Caffarelli–Kohn–Nirenberg inequalities on homogeneous Lie groups.
fractional operator , Homogeneous Lie group , reverse Caffarelli–Kohn–Nirenberg inequality , reverse Hardy inequality , reverse Hardy–Littlewood–Sobolev inequality , reverse Sobolev inequality , reverse Stein–Weiss inequality , Riesz potential
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050040, Kazakhstan
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Department of Mathematics, Nazarbayev University, 53 Kabanbay Batyr Ave, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
School of Mathematical Sciences
Department of Mathematics
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