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Continuity of multilinear operators on Triebel-Lizorkin spaces

Abstract

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.

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References

  1. Chanillo S: A note on commutators. Indiana University Mathematics Journal 1982,31(1):7–16. 10.1512/iumj.1982.31.31002

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen W: A Besov estimate for multilinear singular integrals. Acta Mathematica Sinica. English Series 2000,16(4):613–626. 10.1007/s101140000059

    Article  MathSciNet  MATH  Google 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.1981.30.30053

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohen J, Gosselin JA: On multilinear singular integrals on. Studia Mathematica 1982,72(3):199–223.

    MathSciNet  MATH  Google Scholar 

  5. Cohen J, Gosselin JA: A BMO estimate for multilinear singular integrals. Illinois Journal of Mathematics 1986,30(3):445–464.

    MathSciNet  MATH  Google 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. 10.2307/1970954

    Article  MathSciNet  MATH  Google 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/s101140100113

    Article  MathSciNet  MATH  Google Scholar 

  8. Janson S: Mean oscillation and commutators of singular integral operators. Arkiv för Matematik 1978,16(2):263–270. 10.1007/BF02386000

    Article  MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Lanzhe Liu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Liu, L. Continuity of multilinear operators on Triebel-Lizorkin spaces. J Inequal Appl 2006, 58473 (2006). https://doi.org/10.1155/JIA/2006/58473

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