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arXiv · 2206.10863

Improved Poincar\'e-Hardy inequalities on certain subspaces of the Sobolev space

Debdip Ganguly·Prasun Roychowdhury
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Abstract

We prove an improved version of Poincar\'e-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.

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Debdip Ganguly, Prasun Roychowdhury. 2022-06-22. Improved Poincar\'e-Hardy inequalities on certain subspaces of the Sobolev space. https://doi.org/10.1090/proc%2F16357

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