摘要
It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces L<sup>p<sub>1</sub></sup>×L<sup>p<sub>2</sub></sup>×…× L<sup>p<sub>k</sub></sup>（R<sup>n</sup>） to the Hardy spaces H<sup>T</sup> （R<sup>n</sup>） and the weak Hardy space H<sup>T,∞</sup>（R<sup>n</sup>）. As an application of this result, the L<sup>P</sup>（R<sup>n</sup>） boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.
It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces $L^{p_1 } \times L^{p_2 } \times \cdots \times L^{p_k } (\mathbb{R}^n )$ to the Hardy spacesH r , (? n ) and the weak Hardy spaceH r,∞ (? n . As an application of this result, the L p ,(? n ) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.
基金
Project supported in part by the National Natural Science Foundation of China (Grant No. 19131080) of China
Doctoral Programme Foundation of Institution of Higher Education (Grant No. 98002703) of China
