Boundedness of Multilinear Operators in Herz-type Hardy Space

Let .... We prove that the multilinear operators of finite sums of products of singular integrals on .n are bounded from H\ifmmode\expandafter\else.\expandafter\.\fiK.1,p1q1(Rn)...H\ifmmode\expandafter\else.\expandafter\.\fiK.k,pkqk(Rn) into H\ifmmode\expandafter\else.\expandafter\.\fiK.,pq(Rn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments satisfied by the multilinear operators are also necessary when .j. 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.