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Journal of Function Spaces
Volume 2014 (2014), Article ID 797956, 10 pages
http://dx.doi.org/10.1155/2014/797956
Research Article

Weighted Estimates for Bilinear Operators

1Beijing International Studies University, Beijing 100024, China
2LMAM, School of Mathematical Science, Peking University, Beijing 100871, China

Received 31 May 2013; Accepted 26 November 2013; Published 6 February 2014

Academic Editor: Dashan Fan

Copyright © 2014 Hua Zhu and Heping Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Coifman and L. Grafakos, “Hardy space estimates for multilinear operators,” I, Revista Matemática Iberoamericana, vol. 8, pp. 45–67, 1992. View at Google Scholar
  2. C. Coifman, P. L. Lion, Y. Meyer, and S. Semmes, “Compensated compactness and Hardy spaces,” Journal de Mathématiques Pures et Appliquées, vol. 72, pp. 247–286, 1993. View at Google Scholar
  3. L. Grafakos, “Hardy space estimates for multilinear operators,” Revista Matemática Iberoamericana, vol. 8, pp. 69–92, 1992. View at Google Scholar
  4. C.-C. Lin, Y.-C. Lin, H. Liu, and Y. Liu, “Bilinear operators associated with Schrödinger operators,” Studia Mathematica, vol. 205, no. 3, pp. 281–295, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Garca-Cuerva and K. S. Kazarian, “Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces,” Studia Mathematica, vol. 109, no. 3, pp. 255–276, 1994. View at Google Scholar
  6. J. Stromberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math, Springer, Berlin, Germany, 1989.
  7. T. Quek and D. Yang, “Calderón-zygmund-type operators on weighted weak hardy spaces over ℝn,” Acta Mathematica Sinica, English Series, vol. 16, no. 1, pp. 141–160, 2000. View at Google Scholar · View at Scopus
  8. R. Feerman and F. Soria, “The space weak H1,” Studia Mathematica, vol. 85, pp. 1–16, 1987. View at Google Scholar
  9. H. Liu, The Weak Hp Spaces on Homogeneous Groups, Lecture Notes in Math, Springer, Berlin, Germany, 1991.
  10. J. Alvarez, “Hp and weak Hp continuity of calderón-zygmund type operators, fourier analysis: analytic and geometric aspects,” Marcel Dekker, pp. 17–34, 1994. View at Google Scholar
  11. F. W. Gehring, “The Lp-integrability of the partial derivatives of A quasiconformal mapping,” Acta Mathematica, vol. 130, no. 1, pp. 265–277, 1973. View at Publisher · View at Google Scholar · View at Scopus
  12. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, NY, USA, 1985.
  13. H. Liu, L. Tang, and H. Zhu, “Weighted Hardy spaces and BMO spaces associated with Schrödinger operators,” Mathematische Nachrichten, vol. 285, no. 17-18, pp. 2173–2207, 2012. View at Google Scholar
  14. Z. Shen, “Lp estimates for Schrödinger operators with certain potentials,” Annales de l'institut Fourier, vol. 45, no. 2, pp. 513–546, 1995. View at Google Scholar
  15. J. Dziubański and J. Zienkiewicz, “Hardy space H1 associated to Schrödinger operator with potential satisfying reverse holder inequality,” Revista Matematica Iberoamericana, vol. 15, no. 2, pp. 279–296, 1999. View at Google Scholar · View at Scopus
  16. J. Dziubański, G. Garrigós, T. Martínez, J. L. Torrea, and J. Zienkiewicz, “BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality,” Mathematische Zeitschrift, vol. 249, no. 2, pp. 329–356, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. J. Duoandikoetxea, Fourier Analysis, Graduate Studies in Mathematics, vol. 29, American Mathematical Society, Providence, RI, USA, 2000.
  18. L. Grafakos, Classical and Modern Fourier Analysis, Pearson Edu, New Jersey, NJ, USA, 2004.
  19. E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, USA, 1993.