Science in China Series A: Mathematics

, Volume 48, Issue 4, pp 563–575 | Cite as

Hardy type estimates for commutators of singular integrals

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Abstract

In this paper we study the Hardy type estimates for commutators Tb of standard Calderón-Zygmund singular integral operators T with a Lipschitz function b. The corresponding results are also obtained on the commutators Sb generated by b with singular integral operators S with variable kernels.

Keywords

Calderón-Zygmund singular integrals commutators Lipschitz type spaces Hardy type spaces singular integrals with variable kernels 

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References

  1. 1.
    Coifman, R. R., Rochberg, R., Weiss, G., Factorization theorems for Hardy spaces in several variables, Ann. of Math., 1976, 103: 611–635.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Janson, S., Mean oscillation and commutators of singular integral operators, Ark. Mat., 1978, 16: 263–270.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Harbour, E., Segovia, C., Torrea, J. L., Boundedness of commutators of fractional and singular integrals for the extreme values of p, Ill, J. Math., 1997, 41: 676–700.Google Scholar
  4. 4.
    Pèrez, C., Endpoint estimates for commutators of singular integral operators, J. Func. Anal., 1995, 128: 163–185.MATHCrossRefGoogle Scholar
  5. 5.
    Paluszyński, M., Characterization of the Besov spaces via the commutator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 1995, 44: 1–17.MATHMathSciNetGoogle Scholar
  6. 6.
    Lu, S. Z., Wu, Q., Yang, D. C., Boundedness of commutators on Hardy type spaces, Science in China, Series A, 2002, 45(8): 984–997.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Calderón, A. P., Zygmund, A., Singular integral operators and differential equations, Amer. J. Math., 1957, 79: 801–821.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Chiarenza, F., Frasca, M., Longo, P., Interior estimates for divergence elliptic equations with discontinuos coefficients, Ricerche di Mat., 1991, 40: 149–168.MATHMathSciNetGoogle Scholar
  9. 9.
    Di Fazio, G., L P estimates for divergence form elliptic equations with discontinuous coefficients, Boll. U.M.I., 1996, 10A(7): 409–420.Google Scholar
  10. 10.
    Goldberg, D., A local version of real Hardy spaces, Duke Math. J., 1979, 46: 27–42.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lu, S. Z., Four Lectures on Real H P Spaces, Singapore: World Scientific, 1995.MATHGoogle Scholar
  12. 12.
    Stein, E. M., Harmonic Analysis: Real-variable methods, Orthogobality, and Oscillatory Integrals, Princeton: Princeton Univ. Press, 1993.Google Scholar
  13. 13.
    Stein, E. M., Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton: Princeton Univ. Press, 1971.MATHGoogle Scholar

Copyright information

© Science in China Press 2005

Authors and Affiliations

  1. 1.IMS and Department of MathematicsNanjing UnivetsityNanjingChina

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