高维单位球上两个全纯函数空间之间的复合算子

Composition Opera tors Bet ween Two Holomorphic Function Spaces on the Unit Ball in High Dimension

众所周知,复合算子问题是函数空间的一个基本问题.就一般情形而言,依赖导数刻画的全纯函数空间其复合算子问题要比单复变时复杂。本文讨论了高维单位球上边界一般函数空间F^(p,q,s)(B)到Bloch型空间B^(q+n/p)(B)复合算子有界或紧的充要条件问题,尤其给出了p≠q+n时紧性的简洁充要条件.

It is well known that the problem of composition operator is a basic problem in function spaces.In general,the problem of composition operator for holomorphic function spaces characterized by derivative is much more complicated than that of one complex variable case.In this paper,the authors give the necessary and sufficient condi-tions for the boundedness or compactness of composition opera tors from the boundary general function spaces F^(p,q,s)(B)to the Bloch type spaces B^(q+n/p)(B).In particular,the authors give the simple necessary and sufficient conditions for the compactness of the composition operator when p≠q+n.