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Journal of Function Spaces and Applications
Volume 2013, Article ID 543748, 3 pages
http://dx.doi.org/10.1155/2013/543748
Research Article

Weighted Estimates for Oscillatory Singular Integrals

1Department of Mathematics and Physics, Qatar University, Doha, Qatar
2Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA
3Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received 25 January 2013; Accepted 15 March 2013

Academic Editor: Alberto Fiorenza

Copyright © 2013 H. Al-Qassem et al. 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, “Oscillatory integrals in Fourier analysis,” in Beijing Lectures in Harmonic Analysis, vol. 112 of Annals of Mathematics Studies, pp. 307–355, Princeton University Press, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. Papadimitrakis and I. R. Parissis, “Singular oscillatory integrals on Rn,” Mathematische Zeitschrift, vol. 266, no. 1, pp. 169–179, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Ricci and E. M. Stein, “Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals,” Journal of Functional Analysis, vol. 73, no. 1, pp. 179–194, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Z. Lu and Y. Zhang, “Criterion on Lp-boundedness for a class of oscillatory singular integrals with rough kernels,” Revista Matemática Iberoamericana, vol. 8, no. 2, pp. 201–220, 1992. View at Google Scholar · View at MathSciNet
  5. Y. S. Jiang and S. Z. Lu, “Oscillatory singular integrals with rough kernel,” in Harmonic Analysis in China, vol. 327, pp. 135–145, Kluwer Academic Publishers, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. R. R. Coifman and C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals,” Studia Mathematica, vol. 51, pp. 241–250, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Lu, “A class of oscillatory singular integrals,” International Journal of Applied Mathematical Sciences, vol. 2, no. 1, pp. 47–64, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R. R. Coifman and G. Weiss, “Extensions of Hardy spaces and their use in analysis,” Bulletin of the American Mathematical Society, vol. 83, no. 4, pp. 569–645, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Colzani, Hardy spaces on spheres [Ph.D. thesis], Washington University, St. Louis, Mo, USA, 1982.
  11. J. Duoandikoetxea, “Weighted norm inequalities for homogeneous singular integrals,” Transactions of the American Mathematical Society, vol. 336, no. 2, pp. 869–880, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet