Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
Ruzhansky M. Yessirkegenov N.
15 March 2022Academic Press Inc.
Journal of Mathematical Analysis and Applications
2022#507Issue 2
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of new estimates on hyperbolic spaces. Moreover, in some cases we also show their equivalence with Trudinger-Moser inequalities. As consequences, the relations between the constants of these inequalities are investigated yielding asymptotically best constants in the obtained inequalities. We also obtain the corresponding uncertainty type principles.
Caffarelli-Kohn-Nirenberg inequality , Hardy inequality , Hyperbolic space , Non-positive curvature , Riemannian manifold , Trudinger-Moser inequality
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Suleyman Demirel University, Kaskelen, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Kazakhstan
Department of Mathematics: Analysis
School of Mathematical Sciences
Suleyman Demirel University
Institute of Mathematics and Mathematical Modeling
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