摘要
Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）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 α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.
Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）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 α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.
基金
The second author is partially supported by the NNSF and the SEDF of China
the Grant-in-Aid for Scientific Research (11304009),Japan Society for the Promotion of Science
