Hardy–Sobolev–Rellich, Hardy–Littlewood–Sobolev and Caffarelli–Kohn–Nirenberg Inequalities on General Lie Groups
Ruzhansky M. Yessirkegenov N.
July 2024Springer
Journal of Geometric Analysis
2024#34Issue 7
In this paper, we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy–Littlewood–Sobolev, Caffarelli–Kohn–Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions for an ample class of sub-elliptic differential operators on general connected Lie groups, which include both unimodular and non-unimodular cases in compact and noncompact settings. We also obtain the corresponding uncertainty type principles.
Caffarelli–Kohn–Nirenberg inequality , Hardy inequality , Hardy–Littlewood–Sobolev inequality , Lie groups , Rellich inequality , Sobolev embeddings , Sobolev spaces
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
SDU University, Kaskelen, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis
School of Mathematical Sciences
SDU University
Institute of Mathematics and Mathematical Modeling
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