$L^p$ estimates for oscillatory integral operators
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- by Leslie C. Cheng and Yibiao Pan PDF
- Proc. Amer. Math. Soc. 127 (1999), 2995-3002 Request permission
Abstract:
An endpoint boundedness result is established for a class of oscillatory integral operators.References
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
- José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
- Richard Hunt, Benjamin Muckenhoupt, and Richard Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227–251. MR 312139, DOI 10.1090/S0002-9947-1973-0312139-8
- Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
- Yibiao Pan, Uniform estimates for oscillatory integral operators, J. Funct. Anal. 100 (1991), no. 1, 207–220. MR 1124299, DOI 10.1016/0022-1236(91)90108-H
- Yibiao Pan, Gary Sampson, and PawełSzeptycki, $L^2$ and $L^p$ estimates for oscillatory integrals and their extended domains, Studia Math. 122 (1997), no. 3, 201–224. MR 1434472
- D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1-2, 99–157. MR 857680, DOI 10.1007/BF02392592
- D. H. Phong and E. M. Stein, On a stopping process for oscillatory integrals, J. Geom. Anal. 4 (1994), no. 1, 105–120. MR 1274140, DOI 10.1007/BF02921595
- Fulvio Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179–194. MR 890662, DOI 10.1016/0022-1236(87)90064-4
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
Additional Information
- Leslie C. Cheng
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- Yibiao Pan
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- Received by editor(s): January 8, 1998
- Published electronically: May 3, 1999
- Additional Notes: The second author was supported in part by NSF Grant DMS-9622979
- Communicated by: Christopher D. Sogge
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2995-3002
- MSC (1991): Primary 42A38; Secondary 42A50
- DOI: https://doi.org/10.1090/S0002-9939-99-05048-0
- MathSciNet review: 1625721