本文证明了Ｒｎ上奇异积分乘积之有限和的多线性算子是从ＨＫｑ１α１，ｐ１（Ｒｎ）×… ×ＨＫｑｋαｋ，ｐｋ（Ｒｎ）到ＨＫｑα，ｐ（Ｒｎ）有界的，如果它满足由目标空间所确定的直到一定阶的消失矩条件．这些多线性算子所满足的消失矩条件，当αｊ≥０时也是必要的．而且，这里所考虑的奇异积分包括Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ奇异积分及任意阶的分数次积分．

This paper, the authors prove that the multilinear operators of finite sums of products of singular integrals on Rn are bounded from HK q1α1,p1 (Rn) ×…× HKqkαk,pk(Rn) into HK qα,p(Rn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments satisfying by the multilinear operators are also necessary when αj 0 and the singular integrals considered here include the Calderon-Zygmund singular integrals and the fractional integrals of any orders.