Boundedness of Multilinear Operators in Herz-type Hardy Space

Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singularintegrals on R~n are bounded from H K(R~n)×…×HK(R~n)into HK(R~n)if they havevanishing moments up to a certain order dictated by the target spaces.These conditions on vanishingmoments satisfied by the multilinear operators are also necessary when αand the singular integralsconsidered here include the Calderón-Zygmund singular integrals and the fractional integrals of anyorders.