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http://dx.doi.org/10.4134/JKMS.2011.48.4.703

VECTOR-VALUED INEQUALITIES FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH ROUGH KERNELS  

Tang, Lin (School of Mathematical Sciences Peking University)
Wu, Huoxiong (School of Mathematical Sciences Xiamen University)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 703-725 More about this Journal
Abstract
In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.
Keywords
singular integral; commutator; rough kernel; Fourier transform estimate;
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1 J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Amsterdam-New York, North-Holland, 1985.
2 S. Hofmann, Weighted norm inequalities and vector valued inequalities for certain rough operators, Indiana Univ. Math. J. 42 (1993), no. 1, 1-14.   DOI
3 Y. Hou and L. Tang, $L^p$$(\mathbb{R}^n)$ boundedness for higher commutators of singular integrals with rough kernels belonging to certain block spaces, Math. Nachr. 282 (2009), no. 5, 713-725.   DOI   ScienceOn
4 G. Hu, $L^p$$(\mathbb{R}^n)$ boundedness for the commutators of homogeneous singular integral op- erators, Studia. Math. 154 (2003), no. 1, 13-27.   DOI
5 G. Hu, S. Lu, and B. Ma, Commutators of convolution operators, Acta. Math. Sinica. 42 (1999), no. 2, 359-368.
6 J. Alvarez, R. Bagby R, D. Kurtz, and C. Perez, Weighted estimates for commutators of linear operator, Studia Math. 104 (1993), no. 2, 195-209.   DOI
7 H. Al-Qassem and Y. Pan, Lp estimates for singular integrals with kernels belonging to certain block spaces, Rev. Mat. Iberoamericana. 18 (2002), no. 3, 701-730.
8 A. Al-Salman and Y. Pan, Singular integrals with rough kernels in Llog L$(S^{n-1})$, J. London Math. Soc. 66 (2002), no. 1, 153-174.   DOI
9 K. Andersen and R. John, Weighted inequalities for vector-valued maximal functions and singular integrals, Studia Math. 69 (1980/81), no. 1, 19-31.   DOI
10 S. Lu, M. Taibleson, and G. Weiss, Spaces Generated by Blocks, Beijing Normal Univer- sity Press, 1989.
11 S. Lu and H. Wu, Oscillatory singular integrals and commutators with rough kernels, Ann. Sci. Math. Quebec 27 (2003), no. 1, 47-66.
12 S. Lu and Y. Zhang, Criterion on $L^p$-boundedness for a class of oscillatory singular integrals with rough kernels, Rev. Math. Iberoamericana 8 (1992), no. 2, 201-219.
13 F. Ricci and E. Stein, Harmonic analysis on nilpotent groups and singular integrals I: Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179-194.   DOI
14 H. Triebel, Theory of Function Spaces, Basel, Birkhauser, 1983.
15 D. Watson, Vector-valued inequalities, factorization, and extrapolation for a family of rough operators, J. Funct. Anal. 121 (1994), no. 2, 389-415.   DOI   ScienceOn
16 R. Coifman and Y. Meyer, Avdela des operate pseudo-differentiles, Asterisque. 57 (1978), 1-185.
17 A. P. Calderon and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289-309.   DOI   ScienceOn
18 Y. Chen and Y. Ding, Rough singular integrals on Triebel-Lizorkin space and Besov space, J. Math. Anal. Appl. 347 (2008), no. 2, 493-501.   DOI   ScienceOn
19 J. Chen, H. Jia, and L. Jiang, Boundedness of rough oscillatory singular integral on Triebel-Lizorkin spaces, J. Math, Anal. Appl. 306 (2005), no. 2, 385-397.   DOI   ScienceOn
20 J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc. 336 (1993), no. 2, 869-880.   DOI   ScienceOn
21 J. Duoandikoetxea and J. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimate, Invent. Math. 84 (1986), no. 3, 541-561.   DOI
22 C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107- 115.   DOI   ScienceOn