About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 291397, 7 pages
http://dx.doi.org/10.1155/2014/291397
Research Article

Boundedness of One-Sided Oscillatory Integral Operators on Weighted Lebesgue Spaces

1Department of Mathematics, Linyi University, Linyi 276005, China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
3Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received 6 October 2013; Accepted 9 December 2013; Published 3 February 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2014 Zunwei Fu 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, Harmonic Analysis (Real-variable methods, orthogonality, and oscillatory integrals), vol. 43 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, 1993. View at MathSciNet
  2. L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Upper Saddle River, NJ, USA, 2004. View at MathSciNet
  3. Y. Hu and Y. Pan, “Boundedness of oscillatory singular integrals on Hardy spaces,” Arkiv för Matematik, vol. 30, no. 2, pp. 311–320, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Lu, “Multilinear oscillatory integrals with Calderón-Zygmund kernel,” Science in China A, vol. 42, no. 10, pp. 1039–1046, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. 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. 201–219, 1992. View at MathSciNet
  6. Y. Pan, “Hardy spaces and oscillatory singular integrals,” Revista Matemática Iberoamericana, vol. 7, no. 1, pp. 55–64, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. H. Phong and E. M. Stein, “Singular integrals related to the Radon transform and boundary value problems,” Proceedings of the National Academy of Sciences of the United States of America, vol. 80, no. 24, pp. 7697–7701, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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
  9. 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 Zentralblatt MATH · View at MathSciNet
  10. S. Lu and Y. Zhang, “Weighted norm inequality of a class of oscillatory singular operators,” Chinese Science Bulletin, vol. 37, pp. 9–13, 1992.
  11. E. Sawyer, “Weighted inequalities for the one-sided Hardy-Littlewood maximal functions,” Transactions of the American Mathematical Society, vol. 297, no. 1, pp. 53–61, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weighted inequalities for one-sided maximal functions,” Transactions of the American Mathematical Society, vol. 319, no. 2, pp. 517–534, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. J. Martín-Reyes, L. Pick, and A. de la Torre, “A+ condition,” Canadian Journal of Mathematics, vol. 45, no. 6, pp. 1231–1244, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. J. Martín-Reyes and A. de la Torre, “One-sided BMO spaces,” Journal of the London Mathematical Society, vol. 49, no. 3, pp. 529–542, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Aimar, L. Forzani, and F. J. Martín-Reyes, “On weighted inequalities for singular integrals,” Proceedings of the American Mathematical Society, vol. 125, no. 7, pp. 2057–2064, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Fu, S. Lu, S. Sato, and S. Shi, “On weighted weak type norm inequalities for one-sided oscillatory singular integrals,” Studia Mathematica, vol. 207, no. 2, pp. 137–151, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weights for one-sided operators,” in Recent Development in Real and Harmonic Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 2009.
  18. M. S. Riveros and A. de la Torre, “On the best ranges for Ap+ and RHr+,” Czechoslovak Mathematical Journal, vol. 51, no. 2, pp. 285–301, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. J. Martín-Reyes, “New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions,” Proceedings of the American Mathematical Society, vol. 117, no. 3, pp. 691–698, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. E. M. Stein and G. Weiss, “Interpolation of operators with change of measures,” Transactions of the American Mathematical Society, vol. 87, pp. 159–172, 1958. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet