多圆柱上加权Bergman空间上的Hausdorff伴随算子

Adjoint-Hausdorff Operator on Weighted Bergman Space in the Unit Polydisk

研究Hausdorff伴随算子在加权Bergman空间上的有界性问题,利用Hausdorff伴随算子系数问题到复合算子积分问题的转化,首先证明相应的复合算子在加权Bergman空间上的有界性,然后得到Hausdorff伴随算子的上界估计。

This paper studies the boundedness of adjoint-Hausdorff operator on weighted Bergman space.It transforms the adjoint-Hausdorff operator into an integral of composite operator,and proves the boundedness of this composition operators on weighted Bergman space,then gets the upper bound of the adjoint-Hausdorff operator.