Open Access

Continuity of multilinear operators on Triebel-Lizorkin spaces

Journal of Inequalities and Applications20062006:58473

DOI: 10.1155/JIA/2006/58473

Received: 4 February 2006

Accepted: 28 September 2006

Published: 28 December 2006


The continuity of some multilinear operators related to certain convolution operators on the Triebel-Lizorkin space is obtained. The operators include Littlewood-Paley operator and Marcinkiewicz operator.


Authors’ Affiliations

Department of Mathematics, Changsha University of Science and Technology


  1. Chanillo S: A note on commutators. Indiana University Mathematics Journal 1982,31(1):7–16. 10.1512/iumj.1982.31.31002MathSciNetView ArticleMATHGoogle Scholar
  2. Chen W: A Besov estimate for multilinear singular integrals. Acta Mathematica Sinica. English Series 2000,16(4):613–626. 10.1007/s101140000059MathSciNetView ArticleMATHGoogle Scholar
  3. Cohen J: A sharp estimate for a multilinear singular integral in. Indiana University Mathematics Journal 1981,30(5):693–702. 10.1512/iumj.1981.30.30053MathSciNetView ArticleMATHGoogle Scholar
  4. Cohen J, Gosselin JA: On multilinear singular integrals on. Studia Mathematica 1982,72(3):199–223.MathSciNetMATHGoogle Scholar
  5. Cohen J, Gosselin JA: A BMO estimate for multilinear singular integrals. Illinois Journal of Mathematics 1986,30(3):445–464.MathSciNetMATHGoogle Scholar
  6. Coifman RR, Rochberg R, Weiss G: Factorization theorems for Hardy spaces in several variables. Annals of Mathematics. Second Series 1976,103(3):611–635. 10.2307/1970954MathSciNetView ArticleMATHGoogle Scholar
  7. Ding Y, Lu SZ: Weighted boundedness for a class of rough multilinear operators. Acta Mathematica Sinica. English Series 2001,17(3):517–526. 10.1007/s101140100113MathSciNetView ArticleMATHGoogle Scholar
  8. Janson S: Mean oscillation and commutators of singular integral operators. Arkiv för Matematik 1978,16(2):263–270. 10.1007/BF02386000MathSciNetView ArticleMATHGoogle Scholar
  9. Paluszyński M: Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana University Mathematics Journal 1995,44(1):1–17.MathSciNetMATHGoogle Scholar
  10. Stein EM: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series. Volume 43. Princeton University Press, New Jersey; 1993:xiv+695.Google Scholar
  11. Torchinsky A: Real-Variable Methods in Harmonic Analysis, Pure and Applied Mathematics. Volume 123. Academic Press, Florida; 1986:xii+462.Google Scholar
  12. Torchinsky A, Wang SL: A note on the Marcinkiewicz integral. Colloquium Mathematicum 1990,60/61(1):235–243.MathSciNetMATHGoogle Scholar


© Lanzhe Liu 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.