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


Authors: Ismail Kombe and Murad Özaydin
Journal: Trans. Amer. Math. Soc. 365 (2013), 5035-5050
MSC (2010): Primary 26D10; Secondary 53C21
Published electronically: June 17, 2013
MathSciNet review: 3074365
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Abstract: We continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold $ M$, started in our earlier paper from 2009. In the present paper we prove new weighted Hardy-Poincaré, Rellich type inequalities as well as an 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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Additional Information

Ismail Kombe
Affiliation: Department of Mathematics, Faculty of Science and Letters, Istanbul Commerce University, Selman-1 Pak Cad. No: 2, Üsküdar, Istanbul, Turkey
Email: ikombe@ticaret.edu.tr

Murad Özaydin
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315
Email: mozaydin@math.ou.edu

DOI: https://doi.org/10.1090/S0002-9947-2013-05763-7
Keywords: Hardy-Poincar\'e inequality, Rellich inequality, uncertainty principle inequality
Received by editor(s): May 6, 2011
Published electronically: June 17, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.