Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space

Abstract

We prove an improved version of Poincaré-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Hardy type inequality with an improved constant (than the usual Hardy constant). Furthermore, we derive a new kind of improved Caffarelli-Kohn-Nirenberg inequality on the hyperbolic space.

14 pages

References in corpus (4)

• Non-linear ground state representations and sharp Hardy inequalities
• Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
• Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds
• On Higher order Poincaré Inequalities with radial derivatives and Hardy improvements on the hyperbolic space