The Radon Transform On Quaternion Heisenberg Groups

Let (?)= X × H be the quaternion Heisenberg group,where X denotes the set of all 2 x 2 Pauli matrices and H denotes the quaternion.In this article,the author introduces the Schrodinger representation on the quaternion Heisenberg group 2.Moreover,the author studys the singular convolution operator on (?) via Weyl transform.Furthermore,the author also gives the inverse formula of Radon transform.Finally,the author proves that the Radon transform on (?) is a bounded unitary operator from a Sobolev Space W into L2((?)).