Hardy–Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury
Abstract
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 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.
Topics & Concepts
MathematicsBessel functionHyperbolic spaceRemainderSpace (punctuation)Poincaré conjectureOrder (exchange)Pure mathematicsHardy spaceMathematical analysisArithmeticComputer scienceOperating systemEconomicsFinanceMathematical Analysis and Transform MethodsAdvanced Differential Geometry ResearchDifferential Equations and Boundary Problems