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Acta Mathematica Sinica

, Volume 22, Issue 2, pp 347–356 | Cite as

Multilinear Singular and Fractional Integrals

  • Yong DingEmail author
  • Shan Zhen Lu
  • Kôzô Yabuta
ORIGINAL ARTICLES

Abstract

In this paper, we treat a class of non–standard commutators with higher order remainders in the Lipschitz spaces and give (L p , L q ), (H p , L q ) boundedness and the boundedness in the Triebel– Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.

Keywords

commutators multilinear operators singular and fractional integrals Lp spaces Hardy spaces Lipschitz spaces Triebel–Lizorkin spaces 

MR (2000) Subject Classification

42B20 42B25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P. R. China
  2. 2.School of Science and TechnologyKwansei Gakuin UniversitySanda 669–1337Japan

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