The commutator generated by the Littlewood-Paley operator and the BMO functions are introduced,and the weighted boundedness for the commutator on the Hardy type spaces are obtained by using the atomic decompositions.

• 引入了一类由Littlewood-Paley算子和BMO函数构成的交换子；并利用原子分解的方法证明了该交换子在Hardy型空间上的加权有界性.