JOURNAL BROWSE
Search
Advanced SearchSearch Tips
VECTOR-VALUED INEQUALITIES FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH ROUGH KERNELS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
VECTOR-VALUED INEQUALITIES FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH ROUGH KERNELS
Tang, Lin; Wu, Huoxiong;
  PDF(new window)
 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;
 Language
English
 Cited by
1.
Vector-valued inequalities for the commutators of rough singular kernels, Journal of Inequalities and Applications, 2014, 2014, 1, 139  crossref(new windwow)
 References
1.
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.

2.
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.

3.
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. crossref(new window)

4.
K. Andersen and R. John, Weighted inequalities for vector-valued maximal functions and singular integrals, Studia Math. 69 (1980/81), no. 1, 19-31.

5.
A. P. Calderon and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289-309. crossref(new window)

6.
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. crossref(new window)

7.
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. crossref(new window)

8.
R. Coifman and Y. Meyer, Avdela des operate pseudo-differentiles, Asterisque. 57 (1978), 1-185.

9.
J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc. 336 (1993), no. 2, 869-880. crossref(new window)

10.
J. Duoandikoetxea and J. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimate, Invent. Math. 84 (1986), no. 3, 541-561. crossref(new window)

11.
C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107- 115. crossref(new window)

12.
J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Amsterdam-New York, North-Holland, 1985.

13.
S. Hofmann, Weighted norm inequalities and vector valued inequalities for certain rough operators, Indiana Univ. Math. J. 42 (1993), no. 1, 1-14. crossref(new window)

14.
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. crossref(new window)

15.
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. crossref(new window)

16.
G. Hu, S. Lu, and B. Ma, Commutators of convolution operators, Acta. Math. Sinica. 42 (1999), no. 2, 359-368.

17.
S. Lu, M. Taibleson, and G. Weiss, Spaces Generated by Blocks, Beijing Normal Univer- sity Press, 1989.

18.
S. Lu and H. Wu, Oscillatory singular integrals and commutators with rough kernels, Ann. Sci. Math. Quebec 27 (2003), no. 1, 47-66.

19.
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.

20.
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. crossref(new window)

21.
H. Triebel, Theory of Function Spaces, Basel, Birkhauser, 1983.

22.
D. Watson, Vector-valued inequalities, factorization, and extrapolation for a family of rough operators, J. Funct. Anal. 121 (1994), no. 2, 389-415. crossref(new window)