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Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

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Abstract

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(µ) functions of Tolsa with non-doubling measures is obtained, provided that ∥µ∥ = ∞ and multilinear singular integrals are bounded from L 1(µ) × L 1(µ) to L 1/2,∞(µ).

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References

  1. Grafakos L, Torres R. Multilinear Calderón-Zygmund theory. Adv in Math, 165: 124–164 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Grafakos L, Torres R. On multilinear singular integrals of Calderón-Zygmund type. Publ Math, Extra: 57–91 (2000)

  3. Grafakos L, Torres R. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 51: 1261–1276 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kenig C, Stein E. Multilinear estimates and fractional integration. Math Res Lett, 6: 1–15 (1999)

    MATH  MathSciNet  Google Scholar 

  5. Pérez C, Torres R. Sharp maximal function estimates for multilinear singular integrals. In: Harmonic Analysis at Mount Holyoke, Contemporary Mathematics, 320. Providence: AMS, 2003, 323–331

    Google Scholar 

  6. Hu G, Meng Y, Yang D. Multilinear commutators of singular integrals with non doubling measures. Integral Equations Operator Theory, 51: 235–255 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hu G, Meng Y, Yang D. Multilinear commutators for fractional integrals in non-homogeneous spaces. Publ Mat, 48: 335–367 (2004)

    MATH  MathSciNet  Google Scholar 

  8. Hu G, Meng Y, Yang D. New atomic characterization of H 1 space with non-doubling measures and applications. Math Proc Camb Phil Soc, 138: 151–171 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lin Y, Lu S. Toeplitz operators related to strongly singular Calderón-Zygmund operators. Sci China Ser A-Math, 49: 1048–1064 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Meng Y, Yang D. Boundedness of commutators with Lipschitz functions in non-homogeneous spaces. Taiwanese J Math, 10(6): 1443–1464 (2006)

    MathSciNet  Google Scholar 

  11. Pérez C. Endpoint estimates for commutators of singular integral operators. J Funct Anal, 128: 163–185 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pérez C, Trujillo-Gonzalez R. Sharp weighted estimates for multilinear commutators. J London Math Soc, 65: 672–692 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pérez C, Trujillo-Gonzalez R. Sharp weighted estimates for vector-valued singular integral operators and commutators. Tohoku Math J, 55: 109–129 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sun Y, Su W. Hardy type estimates for commutators of singular integrals. Sci China Ser A-Math, 48: 563–575 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Yang D, Zhou Y. Boundedness of Marcinkiewicz integrals and their commutators in H 1(ℝn × ℝm). Sci China Ser A-Math, 49: 770–790 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Tolsa X. BMO, H 1 and Calderón-Zygmund operators for non doubling measures. Math Ann, 319: 89–101 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Xu J. Boundedness of multilinear singular integrals for non doubling measures. J Math Anal Appl, 327: 481–480 (2007)

    Article  MathSciNet  Google Scholar 

  18. Stein E. Harmonic Analysis. Princeton: Princeton University Press, 1993

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    Jing-shi XU

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  1. Jing-shi XU
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Additional information

This work was partially supported by Scientific Research Fund of Hunan Provincial Education Department (Grant No. 06B059), the Natural Science Foundation of Hunan Province of China (Grant No. 06JJ5012), and the National Natural Science Foundation of China (Grant Nos. 60474070 and 10671062)

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XU, Js. Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures. SCI CHINA SER A 50, 361–376 (2007). https://doi.org/10.1007/s11425-007-2073-1

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  • DOI: https://doi.org/10.1007/s11425-007-2073-1

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