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

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.