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

Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury

Published 2021-06-06Version 1

We prove a family of Hardy-Rellich and Poincar\'e identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Poincar\'e 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.