Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds

Details Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds

2011-03-14

arxiv.org/abs/1103.2747v1

Mathematics

Functional Analysis

Scientific paper

We continue our previous study of improved Hardy, Rellich and Uncertainty principle inequalities on a Riemannian manifold $M$, started in \cite{Kombe-Ozaydin}. In the present paper we prove new weighted Hardy-Poincar\'e, Rellich type inequalities as well as improved version of our Uncertainty principle inequalities on a Riemannian manifold $M$. In particular, we obtain sharp constants for these inequalities on the hyperbolic space $\mathbb{H}^n$.

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