在调和Bergman空间上,给出了径向函数符号的Toeplitz和小Hankel算子乘积为小Hankel算子的充要条件,完全刻画了拟齐次符号小Hankel算子和Toeplitz算子有关乘积或交换子为有限秩的条件.
In this paper,we first give the necessary and sufficient condition for the product of a Toeplitz operator and a small Hankel operator with radial symbols to be a small Hankel operator.Next, we completely characterize the condition for finite rank product or commutator of small Hankel and Toeplitz operators with quasi-homogeneous symbols.