第一类典型域相关联的Radon变换的特征刻画(英文)

The characterization of the Radon transform associated with the classical domain of type one

设D(Ω,Φ)为第一类典型域DI的无界实现,其ilov边界是二步幂零李群.文章首先介绍了上的调和分析相关内容,其中包括给出了群傅里叶变换及Plancherel公式和Plancherel测度等,然后介绍了上的Radon变换,定义了两个施瓦茨函数的子空间,这两个子空间同时是Semyanistyi-Lizorkin空间,Radon变换在这两个子空间上是双射.同时还证明了这两个子空间是等价的.

Let D （ ） be the unbounded realization of the classical domain 79t of type one. In general, its ~ilov boundary 92 is a nilpotent Lie group of step two. In this article we first introduce the harmonic analysis a- bout 92, such as the group Fouriertransform, the Plancherel formula and the Plancherel measure and so on. Then we introduce the Radon transform on 92, and define two subspaces of Schwartz functions Y（92） , which are called the Semyanistyi-Lizorkin type spaces, on which the Radon transform is a bijection. Moreover, we show that these two subspaces are equivalent.