Acta Mathematica Sinica

, Volume 21, Issue 1, pp 209–214

Weak-type Endpoint Estimates for Multilinear Singular Integral Operators

ORIGINAL ARTICLES

Abstract

In this paper, the authors discuss a class of multilinear singular integrals and obtain that the operators are bounded from H1 (ℝn) to weak L1 (ℝn). Using this result, we can directly prove a main theorem in [5].

Keywords

Multilinear integrals Calderón-Zygmund kernel H1 (ℝnBMO (ℝn 

MR (2000) Subject Classification

42B20, 42B25 

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References

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    Pérez, C.: Endpoint estimate for commutators of singular integral operators. J. Funct. Anal., 128, 163–185 (1995)CrossRefMathSciNetGoogle Scholar
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    Chen, W., Hu, G.: Weak type (H 1, L 1) estimate for a multililinear singular integral operator. Advances in Mathematics, 30(1), 63–69 (2001)Google Scholar
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    Christ, M., Rubin de Francia, J. L.: Weak (1,1) bounds for rough operators. Invent. Math., 93, 225–237 (1998)CrossRefMathSciNetGoogle Scholar
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    Lu, S., Yan, D.: L p–boundedness of multilinear oscillatory singular integrals with Calderón–Zygmund kernel. Science in China (Ser. A), 45(2), 196–213 (2002)Google Scholar
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    Lu, S.: Four Lectures on Real H p Spaces, World Scientific, Singapore, New Jersey, London, Hong Kong.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.School of Information Science and Engineering the Graduate School of the Chinese Academy of SciencesBeijing 100080P. R. China
  2. 2.Department of Applied Mathematics University of Information EngineeringZhengzhou 450002P. R. China
  3. 3.Department of Mathematics Lishui Teachers CollegeLishui 323000P. R. China

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