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Rough operators and commutators on homogeneous weighted Herz spaces

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Analysis in Theory and Applications

Abstract

The authors establish the boundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderón-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.

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References

  1. Lu, S. Z. and Yang, D., The Decomposition of Weighted Herz Space onR n and its Applications, Science in China, Ser. A, 38(1995), 147–158.

    MathSciNet  MATH  Google Scholar 

  2. Stein, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. Princeton Univ. Press, Princeton, N. J., 1993.

    MATH  Google Scholar 

  3. Stein, E. M., Note on Singular Integrals, Proc. Amer. Math. Soc., 8(1957), 250–254.

    Article  MathSciNet  Google Scholar 

  4. Soria, F. and Weiss, G., A Remark on Singular Integrals and Power Weights, Indiana Univ. Math., J., 43(1994), 187–204.

    Article  MathSciNet  Google Scholar 

  5. Coifman, R. R., Rochberg, R. and Weiss, G., Fractorization Theorems for Hardy Spaces in Several Variable, Ann. of Math., 103(1976), 611–635.

    Article  MathSciNet  Google Scholar 

  6. Lu, S. Z. & Yang, D., The Continuity of Commutators on Herz-Type Spaces, Michigan Math. J., 44(1997), 255–281.

    Article  MathSciNet  Google Scholar 

  7. Jiang, Y. S., Tang, L. & Yang, D., Continuity of Commutators on Weighted Herz-Type Spaces, Kyushu J. Math., 53(1999), 245–263.

    Article  MathSciNet  Google Scholar 

  8. Hu, G., Lu, S. Z. & Yang, D., Boundedness of Rough Singular Integral Operators on Herz Spaces, J. Austral. Math. Soc. (Series A), 66(1999), 201–223.

    Article  MathSciNet  Google Scholar 

  9. Tang, L., Jiang, Y., & Lu, S. Z., Sublinear Operators on Weighted Herz Spaces, J. Beijing Normal Univ. (Natural Science), 35(1999), 167–173.

    MathSciNet  Google Scholar 

  10. Lu, S. Z., Tang, L., Yang, D., Boundedness of Commutators on Homogeneous Herz Spaces, Science in China, Ser. A, 41(1998), 1023–1033.

    Article  MathSciNet  Google Scholar 

  11. Muckenhoupt B. & Wheeden, R. L., Weighted Norm Inequalities for Singular and Fractional Integrals, Trans. Amer. Math. Soc., 161(1971), 249–258.

    Article  MathSciNet  Google Scholar 

  12. Garcia-Cuerva J. & Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland Math. Studies, Vol. 16, North-Holland, Amsterdam, 1985.

    MATH  Google Scholar 

  13. Hu, G., Weighted Norm Inequalities for Commutators of Homogeneous Singular Integrals, Acta Math. Sinica (New Ser.), 11(1995), 77–88.

    MathSciNet  MATH  Google Scholar 

  14. Alvarez, J., Babgy, R. J., Kurtz, D. S. & Pérez, C., Weighted Estimate for Commutators of Linear Operators, Studia Math., 104(1993), 195–209.

    Article  MathSciNet  Google Scholar 

  15. Watson, D., Weighted Estimates for Singular Integrals Via Fourier Transform Estimates, Duke Math. J., 60(1990), 389–399.

    Article  MathSciNet  Google Scholar 

  16. Jiang, Y. S. and Lu, S. Z., Oscillatory Singular Integral with Rough Kernel, Harmonic Analysis in China, Kluwer Academic Publishers, the Netherlands, 1995, 135–145.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Xinjiang University, 830046, Urumqi, PR China

    Jiang Yinsheng & Liu Mingju

Authors
  1. Jiang Yinsheng
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  2. Liu Mingju
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Corresponding author

Correspondence to Jiang Yinsheng.

Additional information

Project 19871071 supported by Natural Science Foundation of China.

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Yinsheng, J., Mingju, L. Rough operators and commutators on homogeneous weighted Herz spaces. Approx. Theory & its Appl. 18, 51–67 (2002). https://doi.org/10.1007/BF02837048

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  • DOI: https://doi.org/10.1007/BF02837048

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