On Higher order Poincaré Inequalities with radial derivatives and Hardy improvements on the hyperbolic space

Abstract

In this paper we prove higher order Poincaré inequalities involving radial derivatives namely,where underlying space is N -dimensional hyperbolic space H N , 0 ≤ l < k are integers and the constant N−1 2 2(k−l) is sharp. Furthermore we improve the above inequalities by adding Hardytype remainder terms and the sharpness of some constants is also discussed.