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 t...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.展开更多
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 19131080) of ChinaDoctoral Programme Foundation of Institution of Higher Education (Grant No. 98002703) of China
文摘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.
