Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space. (English) Zbl 1525.46022
Summary: 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.
MSC:
| 46E36 | Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 31C12 | Potential theory on Riemannian manifolds and other spaces |
| 33C55 | Spherical harmonics |
| 34B30 | Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) |
| 35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
Keywords:
Hardy inequality; hyperbolic space; spherical harmonics; Bessel pair; Caffarelli-Kohn-Nirenberg inequalitiesReferences:
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