Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs

Abstract

We prove a family of Hardy-Rellich and Poincaré identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Poincaré inequalities. All remainder terms provided considerably improve those already known in literature, and all identities hold with same constants for radial operators also. Furthermore, as applications of the main results, second order versions of the uncertainty principle on the hyperbolic space are derived.

22 Pages

References in corpus (3)

• Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds
• On Higher order Poincaré Inequalities with radial derivatives and Hardy improvements on the hyperbolic space
• The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle

Cited by in corpus (4)

• Multidimensional Frank-Laptev-Weidl improvement of the Hardy Inequality
• Fractional Hardy inequality with singularity on submanifold
• Rellich inequalities via Riccati pairs on model space forms
• Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space