Zero or compact products of several Hankel operators

In this paper we give a necessary and sufficient condition for the product of several Hankel operators on the Hardy space of the unit disk to be zero or compact. This extends results of Brown and Halmos [2], Axler, Chang and Sarason [1], Volberg [8] and Xia and Zheng [9] on zero or compact products of two or three Hankel operators.