中文摘要：

首先证明了加权Bergman空间Aα^2上不变拉普拉斯和Berezin变换是可交换的．其次对稠定义在Aα^2上以平方可积函数f和g为符号的Hankel算子乘积HfHg^＊的有界性给出了一个充分条件．最后完全描述了Aα^2上Hankel算子乘积何时是紧的并且对混合Haplitz乘积也得到了相似结论．

英文摘要：

First, we prove the fact that the invariant Laplacian commutes with the Berezin transform on the weighted Bergman space Aα^2. Secondly, we consider the question for which square integral functions f and g on Aα^2 the densely defined products HfHg^＊ are bounded and give a sufficient condition. Furthermore, We will completely describe when Hankel products on Aα^2 are compact. We also obtain similar results for the mixed Haplitz products HgTg and TfHg^＊, where f and g are square integrable on the unit disk and f is analytic.