Nagoya Mathematical Journal

Hardy spaces estimates for multilinear operators with homogeneous kernels

Yong Ding and Shanzhen Lu

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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.

Article information

Nagoya Math. J., Volume 170 (2003), 117-133.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 47G10: Integral operators [See also 45P05]


Ding, Yong; Lu, Shanzhen. Hardy spaces estimates for multilinear operators with homogeneous kernels. Nagoya Math. J. 170 (2003), 117--133.

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