Boundedness of Multilinear Operators in Herz-type Hardy Space

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.