关于S^p空间上加权复合算子的有界性

On the Boundedness of Weighted Composition Operators on S^p Spaces

S^p(1≤p≤∞)空间为导数属于Hardy空间H^p的复平面单位圆盘Δ上所有解析函数组成的空间。令函数φ和ф是Δ上的解析函数且φ(Δ)Δ,则将算子Wφ,ф∶f aф(foφ)称为加权复合算子。文章给出了当φ是Δ上的共形满射时该加权复合算子Wφ,ф在S^p空间上的有界性的充要条件。

S^p（1≤p≤∞） is the space of all analytic functions on the unit disk Δ whose derivatives belong to the Hardy space H^p. If φ and ф are two analytic functions defined on Δ and φ（Δ） Δ,then the operator defined by Wφ,ф∶f aф（f o φ） is called the weighted composition operator. This paper discusses about the necessary and sufficient conditions for the boundedness of Wφ,on SPwhen φ is a conformal mapping of Δ onto itself.