Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 158281, 17 pages
doi:10.1155/2010/158281
Research Article

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Yongyang Jin1 and Yazhou Han2

1Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
2Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018, China

Received 19 March 2010; Accepted 15 June 2010

Academic Editor: Nikolaos Papageorgiou

Copyright © 2010 Yongyang Jin and Yazhou Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove a sharp weighted Rellich inequality associated with a class of Greiner-type vector fields on H-type groups. We also obtain some weighted Hardy- and Rellich-type inequalities on nonisotropic Heisenberg groups. As an application, we get a Rellich-Sobolev-type inequality on Heisenberg groups.