Radon transforms on Siegel-type nilpotent Lie groups

Abstract

Let $$\mathfrak{N}:=H_n\times\mathbb{C}^n$$ be the Siegel-type nilpotent group, which can be identified as the Shilov boundary of Siegel domain of type II, where Hn denotes the set of all n × n Hermitian matrices. In this article, we use singular convolution operators to define Radon transform on $$\mathfrak{N}$$ and obtain the inversion formulas of Radon transforms. Moveover, we show that Radon transform on $$\mathfrak{N}$$ is a unitary operator from Sobolev space Wn,2 into $$L^2(\mathfrak{N})$$ .