C^n中μ-Bergman空间的刻画和微分复合算子

Characterizations and Differentiation Composition Operators of μ-Bergman Space in C^n

设p>0,μ和μ_1是[0,1)上的正规函数.本文首先给出了C^n中单位球上μ-Bergman空间A^p(μ)的几种等价刻画;然后分别刻画了A^p(μ)到A^p(μ_1)的微分复合算子D_φ为有界算子以及紧算子的充要条件,同时给出了当p>1时D_φ为A^p(μ)到A^p(μ_1)上紧算子的一种简捷充分条件和必要条件.

Let p 〉 0, μ and μ1 be two normal functions on [0, 1）. In this paper, a kind of equivalent characterizations of the p-Bergman space on the unit ball in Cn are given first. Furthermore, the necessary and sufficient conditions that the differentiation composition operator Dφ is a bounded operator or a compact operator from AP（p） to AP（μ1） are given, respectively. At the same time, a simple sufficient condition and the necessary condition that Dφ is a compact operator from AP（μ） to AP（μ1） are given.