Acta Mathematica Sinica, English Series

, Volume 26, Issue 4, pp 603–620 | Cite as

Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals

  • Yong Ding
  • Guo Zhen Lu
  • Bo Lin MaEmail author


Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.


flag singular integrals multiparameter Triebel-Lizorkin spaces discrete Calderón reproducing formulas discrete Littlewood-Paley-Stein analysis 

MR(2000) Subject Classification

42B35 42B25 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems (BNU)Ministry of EducationBeijingP. R. China
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA
  3. 3.College of Mathematics and Information EngineeringJiaxing UniversityJiaxingP. R. China
  4. 4.School of MathematicsBeijing Normal UniversityBeijingP. R. China

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