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Abstract and Applied Analysis
Volume 2013, Article ID 651941, 15 pages
http://dx.doi.org/10.1155/2013/651941
Research Article

Boundedness for Parametrized Littlewood-Paley Operators with Rough Kernels on Weighted Weak Hardy Spaces

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Received 27 April 2013; Accepted 18 June 2013

Academic Editor: Dashan Fan

Copyright © 2013 Ximei Wei and Shuangping Tao. 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. E. M. Stein, “The development of square functions in the work of A. Zygmund,” Bulletin of the American Mathematical Society, vol. 7, no. 2, pp. 359–376, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. C. E. Kenig, Harmonic Ayalysis Techniques for Second Order Elliptic Boundary Value Problems, vol. 83 of CBMS, American Mathematical Society, 1991.
  3. S.-Y. A. Chang, J. M. Wilson, and T. H. Wolff, “Some weighted norm inequalities concerning the Schrödinger operators,” Commentarii Mathematici Helvetici, vol. 60, no. 2, pp. 217–246, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Fefferman and E. M. Stein, “Hp spaces of several variables,” Acta Mathematica, vol. 129, no. 3-4, pp. 137–193, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C. Fefferman and E. M. Stein, “Some maximal inequalities,” American Journal of Mathematics, vol. 93, pp. 107–115, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. E. M. Stein, “On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz,” Transactions of the American Mathematical Society, vol. 88, pp. 430–466, 1958. View at Publisher · View at Google Scholar · View at MathSciNet
  7. E. M. Stein, “On some funcions of Littlewood-Paley and Zygmund,” Bulletin of the American Mathematical Society, vol. 67, pp. 99–101, 1961. View at Publisher · View at Google Scholar · View at MathSciNet
  8. E. M. Stein, Singular integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, USA, 1970. View at MathSciNet
  9. L. Hörmander, “Estimates for translation invariant operators in Lp spaces,” Acta Mathematica, vol. 104, pp. 93–140, 1960. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Sakamoto and K. Yabuta, “Boundedness of Marcinkiewicz functions,” Studia Mathematica, vol. 135, no. 2, pp. 103–142, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Y. Ding, S. Z. Lu, and K. Yabuta, “A problem on rough parametric Marcinkiewicz functions,” Journal of the Australian Mathematical Society, vol. 72, no. 1, pp. 13–21, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Ding, S. Z. Lu, and Q. Y. Xue, “Parametrized area integrals on Hardy spaces and weak Hardy spaces,” Acta Mathematica Sinica (English Series), vol. 23, no. 9, pp. 1537–1552, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Ding, S. Z. Lu, and Q. Y. Xue, “Parametrized Littlewood-Paley operators on Hardy and weak Hardy spaces,” Mathematische Nachrichten, vol. 280, no. 4, pp. 351–363, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. B. Wang and Z. G. Liu, “Weighted estimates for parametrized Littlewood-Paley operators,” Frontiers of Mathematics in China, vol. 6, no. 3, pp. 517–534, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. Wang, “Boundedness of intrinsic square functions on the weighted weak Hardy spaces,” Integral Equations and Operator Theory, vol. 75, no. 1, pp. 135–149, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. C. Fefferman, N. M. Rivière, and Y. Sagher, “Interpolation between Hp spaces: the real method,” Transactions of the American Mathematical Society, vol. 191, pp. 75–81, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. Fefferman and F. Soria, “The space H1,” Studia Mathematica, vol. 85, no. 1, pp. 1–16, 1987. View at Google Scholar · View at MathSciNet
  18. H. P. Liu, “The weak Hp spaces on homogeneous groups,” in Harmonic analysis, Lecture Notes in Math., pp. 113–118, Springer, Berlin, Germany, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. T. S. Quek and D. C. Yang, “Calderón-Zygmund-type operators on weighted weak Hardy spaces over n,” Acta Mathematica Sinica (English Series), vol. 16, no. 1, pp. 141–160, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal function,” Transactions of the American Mathematical Society, vol. 165, pp. 207–226, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, The Netherlands, 1985. View at MathSciNet
  22. Y. Ding and Q. Y. Xue, “Weighted Lp boundedness for parametrized Littlewood-Paley operators,” Taiwanese Journal of Mathematics, vol. 11, no. 4, pp. 1143–1165, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Y. Ding and S. Z. Lu, “Homogeneous fractional integrals on Hardy spaces,” The Tohoku Mathematical Journal, vol. 52, no. 1, pp. 153–162, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet