关键词: Bergman空间, Berezin变换, 紧算子

Abstract: Let L^p_a(Dⁿ) denote the analytic functions on the unit polydisk Dⁿ that are also pintegrable. By using polydisk function theory and Schur estimate, we studied the charactarization of compactness of a bounded operator S on the Bergman space L^p_a(Dⁿ) 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. We extended the description of operators’ compactness in one complex variable to that in several complex variables.

Key words: Bergman space, Berezin transform, compact operator