Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ENDPOINT ESTIMATES FOR MULTILINEAR INTEGRAL OPERATORS

  • Lanzhe, Liu (DEPARTMENT OF MATHEMATICS CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Published : 2007.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the endpoint estimates for some multilinear operators related to certain integral operators are obtained. The operators include Littlewood-Paley operators and Marcinkiewicz operators.

Keywords

References

  1. J. Alvarez, R. J. Babgy, D. S. Kurtz, and C. Perez, Weighted estimates for commutators of linear operators, Studia Math. 104 (1993), no. 2, 195-209 https://doi.org/10.4064/sm-104-2-195-209
  2. W. G. Chen and G. E. Hu, Weak type ($H^{1}$, $L^{1}$) estimate for multilinear singular integral operator, Adv. Math. (China) 30 (2001), no. 1, 63-69
  3. J. Cohen, A sharp estimate for a multilinear singular integral on $R^n$, Indiana Univ. Math. J. 30 (1981), no. 5, 693-702 https://doi.org/10.1512/iumj.1981.30.30053
  4. J. Cohen and J. Gosselin, On multilinear singular integral operators on Rn, Studia Math. 72 (1982), no. 3, 199-223 https://doi.org/10.4064/sm-72-3-199-223
  5. J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integrals, Illinois J. Math. 30 (1986), no. 3, 445-464
  6. R. Coifman and Y. Meyer, Wavelets, Calderon-Zygmund and multilinear operators, Cambridge Studies in Advanced Math. 48, Cambridge University Press, Cambridge, 1997
  7. J. Garcia-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), no. 3, 499-513 https://doi.org/10.1112/jlms/s2-39.3.499
  8. J. Garcia-Cuerva and M. L. Herrero, A theory of Hardy spaces associated to the Herz spaces, Proc. London Math. Soc. 69 (1994), no. 3, 605-628 https://doi.org/10.1112/plms/s3-69.3.605
  9. J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Math. 16, Amsterdam, 1985
  10. E. Harboure, C. Segovia, and J. L. Torrea, Boundedness of commutators of fractional and singular integrals for the extreme values of p, Illinois J. Math. 41 (1997), no. 4, 676-700
  11. L. Z. Liu, Weighted weak type ($H^{1}$, $L^{1}$) estimates for commutators of Littlewood-Paley operator, Indian J. of Math. 45 (2003), no. 1, 71-78
  12. L. Z. Liu, Endpoint estimates for multilinear Marcinkiewicz integral operators, East J. Approx. 9 (2003), no. 3, 339-350
  13. L. Z. Liu, Weighted Block-$H^1$ estimates for commutators of Littlewood-Paley operators, Southeast Asian Bull. Math. 27 (2004), no. 5, 833-838
  14. S. Z. Lu and D. C. Yang, The decomposition of the weighted Herz spaces on $R^{n}$ and its applications, Sci. China Ser. A 38 (1995), no. 2, 147-158
  15. S. Z. Lu and D. C. Yang, The weighted Herz type Hardy spaces and its applications, Sci. China Ser. A 38 (1995), no. 6, 662-673
  16. E. M. Stein, Harmonic Analysis: real variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993
  17. A. Torchinsky, Real-variable methods in harmonic analysis, Pure and Applied Math. 123, Academic Press, New York, 1986
  18. A. Torchinsky and S. Wang, A note on the Marcinkiewicz integral, Colloq. Math. 60/61 (1990), no. 1, 235-243