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On the commutators of singular integrals related to block spaces

Published online by Cambridge University Press:  22 January 2016

Shanzhen Lu  and
Huoxiong Wu
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing, 100875, P. R. China, lusz@bnu.edu.cn
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China, huoxwu@xmu.edu.cn
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Abstract

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In this paper, the commutators of singular integrals with rough kernels are considered. By the method of block decomposition for kernel function and Fourier transform estimates, some new results about the Lp(ℝn) boundedness for these commutators are obtained.

Keywords

42B2047B2042B3547A30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 173 , 2004 , pp. 205 - 223
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[1] AL-Hasan, A.J. and Fan, D. S., A singular integral operator related block spaces, Hokkaido Math. J., 28 (1999), 285–299.CrossRefGoogle Scholar
[2] Alvarez, J., Bagby, R., Kurtz, D. and Pérez, C., Weighted estimates for commutators of linear operators, Studia Math., 104 (1993), 195–209.CrossRefGoogle Scholar
[3] Coifman, R. and Rochberg, R., Another characterization of BMO, Proc. Amer. Math. Soc., 79(2) (1980), 249–254.Google Scholar
[4] Coifman, R., Rochberg, R. and Weiss, G., Factorization theorems for Hardy spaces in several variables, Ann. of Math., 103 (1976), 611–636.Google Scholar
[5] Calderon, A.P. and Zygmund, A., On singular integrals, Amer. J. Math., 78 (1956), 289–309.Google Scholar
[6] Duoandikoetxea, J., Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc., 336 (1993), 869–880.Google Scholar
[7] Duoandikoetxea, J. and Francia, J.L. Rubio de, Maximal and singular integral oper ators via Fourier transform estimates, Invent. Math., 84 (1996), 541–561.Google Scholar
[8] Garcia-Cuerva, J., Harboure, E., Segovia, C. and Torre, J. L., Weighted norm inequali ties for commutators of strongly singular integrals, Indiana Univ. Math. J., 40 (1991), 1397–1420.Google Scholar
[9] Hu, G.E., L2-boundedness for the commutators with convolution operators, Nagoya Math.J., 163 (2001), 55–70.Google Scholar
[10] Hu, G.E., Weighted norm inequalities for commutators of homogeneous singular inte gral operators, Acta Math. Sinica, New series, 11 (1995), Special Issue: 77–88.Google Scholar
[11] Hu, G.E., Lu, S. Z. and Ma, B. L., The commutators of convolution operators (in Chinese), Acta Math. Sinica, 42 (1999), 359–368.Google Scholar
[12] Hu, G.E. and Ma, B. L., L2(ℝn) boundedness for the commutators of homogeneous singular integral operators, Acta Math. Sinica (to appear).Google Scholar
[13] Hu, G.E. and Sun, Q. Y., Lp boundedness for the commutators of convolution operators, Chinese Ann. of Math. (Ser. A), 22(4) (2001), 509–516.Google Scholar
[14] Keitoku, M. and Sato, S., Block spaces on the unit sphere in ℝn , Proc. Amer. Math. Soc., 119 (1993), 453–455.Google Scholar
[15] Lu, S.Z., Taibleson, M. and Weiss, G., Spaces Generated by Blocks, Beijing Normal University Press, Beijing, 1989.Google Scholar
[16] Lu, S.Z. and Wu, H. X., Oscillatory singular integrals and commutators with rough kernels, Ann. Sci. Math. Québec, 27(1) (2003), 47–66.Google Scholar
[17] Taibleson, M.H. and Weiss, G., Certain function spaces associated with a.e. convergence of Fourier series, Univ. of Chicago Conf. in honor of Zygmund, Vol.I, Woodsworth, 1983, 95–113.Google Scholar