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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Improved Hardy and Rellich inequalities on Riemannian manifolds


Authors: Ismail Kombe and Murad Özaydin
Journal: Trans. Amer. Math. Soc. 361 (2009), 6191-6203
MSC (2000): Primary 26D10; Secondary 53C21
Published electronically: July 22, 2009
MathSciNet review: 2538592
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Abstract: In this paper we establish improved Hardy and Rellich type inequalities on a Riemannian manifold $ M$. Furthermore, we also obtain sharp constants for improved Hardy and Rellich type inequalities on the hyperbolic space $ \mathbb{H}^n$.


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Additional Information

Ismail Kombe
Affiliation: Department of Mathematics, Dawson-Loeffler Science & Mathematics Bldg., Oklahoma City University, 2501 N. Blackwelder, Oklahoma City, Oklahoma 73106-1493
Email: ikombe@okcu.edu

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

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04642-X
PII: S 0002-9947(09)04642-X
Keywords: Hardy inequality, Rellich inequality, sharp constants
Received by editor(s): March 13, 2007
Published electronically: July 22, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.