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Hardy spaces estimates for a class of multilinear homogeneous operators

Authors:	Yong Ding Shanzhen Lu

Institution:	(1) Department of Mathematics, Beijing Normal University, 100875 Beijing, China

Abstract:	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, (ℝⁿ) and the weak Hardy spaceH ^r,∞ (ℝⁿ. As an application of this result, the L^p,(ℝⁿ) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained. Project supparted in part by the National Natural Science Foundation of Chind (Grant No. 19131080) of China and Doctoral Programme Foundation of Institution of Higher Education (Grant No. 98002703) of China.

Keywords:	multilinear operator singular integral L^s-Dini conditon H ^r andH ^r-∞ space
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