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Commutators Estimates on Triebel–Lizorkin Spaces

Published online by Cambridge University Press:  20 November 2018

Liya Jiang ,
Houyu Jia  and
Han Xu
Liya Jiang
Affiliation:
Department of Mathematics, Zhejiang University, P.R. China, and Department of Mathematics, Zhejiang University of Technology, P.R. China e-mail: mathjly@163.com
Houyu Jia
Affiliation:
Department of Mathematics, Zhejiang University, P.R. China e-mail: mjhy@zju.edu.cn
Han Xu
Affiliation:
Department of Mathematics, Zhejiang University of Sciences, P.R. China e-mail: xuhan@zjst.edu.cn
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Abstract

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In this paper, we consider the behavior of the commutators of convolution operators on the Triebel–Lizorkin spaces ${{\dot{F}}_{p}}^{s,q}$.

Keywords

42B46FcommutatorsTriebel–Lizorkin spacesparaproduct
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 3 , 01 September 2006 , pp. 414 - 427
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Alvarez, J., Bagby, R., Kurtz, D., and Pérez, C., Weighted estimates for commutators of linear operators. Studia Math. 104(1993), 195–209.Google Scholar
[2] Chen, J., Fan, D., and Ying, Y., Singular integral operators on function spaces. J. Math. Anal. Appl. 276(2002), 691–708.Google Scholar
[3] Coifman, R., Lions, P. L., Meyer, Y., and Semmes, S., Compensated compactness and Hardy spaces. J. Math. Pures Appl. 72(1993), no. 3, 247–286.Google Scholar
[4] Coifman, R. and Meyer, Y., Au déla des opérateurs pseudo-différentiels, Astérisque 57 Société Mathématique de France, Paris, 1978.Google Scholar
[5] Coifman, R., Rochberg, R., and Weiss, G., Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103(1976), no. 3, 611–635.Google Scholar
[6] Duoandikoetxea, J., Weighted norm inequalities for homogeneous singular integrals. Trans. Amer. Math, Soc. 336(1993), no. 2, 869–880.Google Scholar
[7] Frazier, M. and Jawerth, B., A discrete transform and applications to distribution spaces. J. Funct. Anal. 93(1990), no. 1, 34–170.Google Scholar
[8] Frazier, M., Torres, R., and Weiss, G., The boundedness of Calderon-Zygmund operators on spaces. Rev. Mat. Iberoammericana 4(1988), no. 1, 41–72.Google Scholar
[9] Garcia-Cuerva, J. and de Francia, J. L. Rubio, Weighted Norm Inequalities and Related Topics. North Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985.Google Scholar
[10] Hu, G., L 2 (R n ) Boundedness for the commutators of convolution Operators. Nagaya Math. J. 163(2001), 55–70.Google Scholar
[11] Hu, G., Lu, S., and Ma, B., Commutators of convolution operators (in Chinese). Acta Math. Sinica, 42(1999), no. 2, 359–368.Google Scholar
[12] Torres, R., Boundedness Results for Operators With Singular Kernels on Distribution Spaces. Mem. Amer.Math. Soc. 90, Providence, RI, no. 442, 1991.Google Scholar
[13] Triebel, H., Theory of Function Spaces. II. Monographs in Mathematics 84, Birkhäuser Verlag, Basel. 1992.Google Scholar
[14] Youssfi, A., Commutators on Besov spaces and factorization of the paraproduct. Bull. Sci. Math. 119(1995), no. 2, 157–186.Google Scholar