单位多圆盘上加权Bergman空间上的紧算子

Compact Operators on Weighted Bergman Spaces of the Unit Polydiscs

记Apψ(Dn)(P>1)为单位多圆盘Dn上P次可积解析函数全体组成的加权Bergman空间．该文利用多圆盘函数论及Schur估计,研究了加权Bergman空间Apψ(Dn)上有界算子S满足一定可积条件时的紧性刻画,证明了S为紧的当且仅当其Berezin变换在多圆盘的边界趋于零．

Let Aφ^p（D^n）（p〉 1） denote the Banach space consisting of all analytic functions in the unit polydisk D^n that are also p--integrable, In this paper, by using polydisk function thoery and Sehur test, we studied eharactarization of compactness of a bounded operator S on the weighted Bergman space Aφ^p（ D^n ） if S satisfied some integrable conditions, and proved that S is compact if and only if its Berezin transform vanishes on the boundary of the unit polydisk,