Abstract
In this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional 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 spaces $H^q({\mathbb R}^n)$ and the weak Hardy space $H^{q,\infty}({\mathbb R}^n)$, where the kernel functions $\Omega_{ij}$ satisfy only the $L^s$-Dini conditions. As an application of this result, we obtain the $(L^p, L^q)$ boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.
Citation
Yong Ding. Shanzhen Lu. "Hardy spaces estimates for multilinear operators with homogeneous kernels." Nagoya Math. J. 170 117 - 133, 2003.
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