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Hardy spaces estimates for multilinear operators with homogeneous kernels

Published online by Cambridge University Press:  22 January 2016

Yong Ding  and
Shanzhen Lu
Yong Ding
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, China, dingy@bnu.edu.cn
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, China, lusz@bnu.edu.cn
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Abstract

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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 Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

Keywords

42B2547G10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 117 - 133
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

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