Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SHARP WEIGHTED ESTIMATE FOR MULTILINEAR SINGULAR INTEGRAL OPERATOR

  • Lanzhe, Liu (College of Mathematics Changsha University of Science and Technology)
  • Published : 2006.07.01
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Abstract

In this paper, a sharp inequality for some multilineal singular integral operators are obtained. As the applications, we get the weighted $L^p(p>1)$ norm inequalities and L log L type estimate for the multilinear operators.

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References

  1. J. Cohen, A sharp estimate for a multilinear singular integral on $R^n$, Indiana Univ. Math. J. 30 (1981), 693-702 https://doi.org/10.1512/iumj.1981.30.30053
  2. J. Cohen and J. Gosselin, On multilinear singular integral operators on $R^n$, Studia Math. 72 (1982), 199-223 https://doi.org/10.4064/sm-72-3-199-223
  3. J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integral operators, Illinois J. Math.30 (1986), 445-465
  4. R. Coifman and Y. Meyer, Wavelets, Calderon-Zygmund and multilinear operators, Cambridge Studies in Advanced Math. 48, Cambridge University Press, Cambridge, 1997
  5. Y. Ding and S. Z. Lu, Weighted boundedness for a class rough multilinear operators, Acta Math. Sinica 17 (2001), 517-526 https://doi.org/10.1007/s101140100113
  6. J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm -inequalit-ies and related topics, North-Holland Math. 16, Amsterdam, 1985
  7. G. Hu and D. C. Yang, A variant sharp estimate for multilinear singular integral operators, Studia Math. 141 (2000), 25-42 https://doi.org/10.4064/sm-141-1-25-22
  8. C. Perez, Endpoint estimate for commutators of singular integral operators, J. Func. Anal. 128 (1995), 163-185 https://doi.org/10.1006/jfan.1995.1027
  9. C. Perez, Sharp estimates for commutators of s-ingular inteqrols via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl. 3 (1997), 743-756 https://doi.org/10.1007/BF02648265
  10. C. Perez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J. 49 (2001), 23-37 https://doi.org/10.1307/mmj/1008719033
  11. C. Perez and R. Trujillo-Gonzalez, Sharp we-ighted estimates for multilinear commutators, J. London Math. Soc. 65 (2002), 672-692 https://doi.org/10.1112/S0024610702003174
  12. E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993