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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 291397, 7 pages
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.
- 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.
- L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Upper Saddle River, NJ, USA, 2004.
- Y. Hu and Y. Pan, “Boundedness of oscillatory singular integrals on Hardy spaces,” Arkiv för Matematik, vol. 30, no. 2, pp. 311–320, 1992.
- S. Lu, “Multilinear oscillatory integrals with Calderón-Zygmund kernel,” Science in China A, vol. 42, no. 10, pp. 1039–1046, 1999.
- S. Lu and Y. Zhang, “Criterion on -boundedness for a class of oscillatory singular integrals with rough kernels,” Revista Matemática Iberoamericana, vol. 8, no. 2, pp. 201–219, 1992.
- Y. Pan, “Hardy spaces and oscillatory singular integrals,” Revista Matemática Iberoamericana, vol. 7, no. 1, pp. 55–64, 1991.
- 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.
- 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.
- R. R. Coifman and C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals,” Studia Mathematica, vol. 51, pp. 241–250, 1974.
- S. Lu and Y. Zhang, “Weighted norm inequality of a class of oscillatory singular operators,” Chinese Science Bulletin, vol. 37, pp. 9–13, 1992.
- 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.
- 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.
- F. J. Martín-Reyes, L. Pick, and A. de la Torre, “ condition,” Canadian Journal of Mathematics, vol. 45, no. 6, pp. 1231–1244, 1993.
- 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.
- 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.
- 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.
- 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.
- M. S. Riveros and A. de la Torre, “On the best ranges for and ,” Czechoslovak Mathematical Journal, vol. 51, no. 2, pp. 285–301, 2001.
- 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.
- 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.