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Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space (2206.10863v1)
Published 22 Jun 2022 in math.AP
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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