Bounded Hankel Products On Bergman Space In The Unit Ball

In this paper,the necessary condition and sufficient condition for the boundedness of the densely defined Hankel products H_fH_g^* on the Bergman space of the unit ball is investigated,where f and g are square integrable on the unit ball.Furthermore similar results for the mixed Haplitz products H_fT_(?) and T_gH_f^* are obtained by the same methods when g is holomorphic on the unit ball.In partial,a necessary and sufficient condition also obtained for the product H_fH_g^* to be bounded if f and g are bounded functions in the unit ball.The paper is divided into seven parts.In the first part,we mainly talk about the background of this paper,and point out some primary works in this field in recent years.In the second part,some basic concept and conclusion which will be used in this paper is briefly introduced.At the same time,the primary theorems are given.In the third part,some lemmas which are necessary to this paper are given and proved.The next three parts are the proof of the primary theorems.At last,we summarize the work of the whole paper and give some open problems.