On oscillatory integral operators with folding canonical relations

 Access to full text

 Full (PDF)

1. [1] J. Bourgain, Estimations de certaines fonctions maximales, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), 499-502. 
2. [2] A. P. Calderón and R. Vaillancourt, A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185-1187. Zbl0244.35074
3. [3] A. Carbery, A. Seeger, S. Wainger and J. Wright, Classes of singular integral operators along variable lines, J. Geom. Anal., to appear. Zbl0964.42003
4. [4] M. Christ, Failure of an endpoint estimate for integrals along curves, in: Fourier Analysis and Partial Differential Equations, J. García-Cuerva, E. Hernandez, F. Soria and J. L. Torrea (eds.), Stud. Adv. Math., CRC Press, 1995, 163-168. Zbl0871.42017
5. [5] A. Comech, Oscillatory integral operators in scattering theory, Comm. Partial Differential Equations 22 (1997), 841-867. Zbl0883.35142
6. [6] S. Cuccagna, $L^2$ estimates for averaging operators along curves with two-sided k-fold singularities, Duke Math. J. 89 (1997), 203-216. Zbl0908.47050
7. [7] A. Greenleaf and A. Seeger, Fourier integral operators with fold singularities, J. Reine Angew. Math. 455 (1994), 35-56. Zbl0799.42008
8. [8] A. Greenleaf and A. Seeger, Fourier integral operators with simple cusps, Amer. J. Math., to appear. 
9. [9] A. Greenleaf and G. Uhlmann, Estimates for singular Radon transforms and pseudo-differential operators with singular symbols, J. Funct. Anal. 89 (1990), 202-232. Zbl0717.44001
10. [10] L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79-183. Zbl0212.46601
11. [11] L. Hörmander, Oscillatory integrals and multipliers on $F{L}^p$, Ark. Mat. 11 (1973), 1-11. Zbl0254.42010
12. [12] R. Melrose and M. Taylor, Near peak scattering and the correct Kirchhoff approximation for a convex obstacle, Adv. Math. 55 (1985), 242-315. Zbl0591.58034
13. [13] Y. Pan, Hardy spaces and oscillatory integral operators, Rev. Mat. Iberoamericana 7 (1991), 55-64. 
14. [14] Y. Pan, Hardy spaces and oscillatory integral operators, II, Pacific J. Math. 168 (1995), 167-182. 
15. [15] Y. Pan and C. D. Sogge, Oscillatory integrals associated to folding canonical relations, Colloq. Math. 61 (1990), 413-419. Zbl0746.58076
16. [16] D. H. Phong, Singular integrals and Fourier integral operators, in: Essays on Fourier Analysis in Honor of Elias M. Stein (C. Fefferman, R. Fefferman and S. Wainger, eds.), Princeton Math. Ser. 42, Princeton Univ. Press, 1995, 286-320. 
17. [17] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals and Radon transforms I, Acta Math. 157 (1986), 99-157. Zbl0622.42011
18. [18] D. H. Phong and E. M. Stein, Radon transforms and torsion, Internat. Math. Res. Notices 4 (1991), 49-60. Zbl0761.46033
19. [19] D. H. Phong and E. M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. 140 (1994), 703-722. Zbl0833.43004
20. [20] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals I. Oscillatory integrals, J. Funct. Anal. 73 (1987), 179-194. Zbl0622.42010
21. [21] A. Seeger, Degenerate Fourier integral operators in the plane, Duke Math. J. 71 (1993), 685-745. Zbl0806.35191
22. [22] H. Smith and C. D. Sogge, $L^p$ regularity for the wave equation with strictly convex obstacles, Duke Math. J. 73 (1994), 97-153. Zbl0805.35169
23. [23] E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Princeton Univ. Press, Princeton, N.J., 1986, 307-356. 
24. [24] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993. Zbl0821.42001
25. [25] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971. Zbl0232.42007