Local smoothing of Fourier integral operators and Carleson-Sjölin estimates

Mockenhaupt, Gerd ; Seeger, Andreas ; Sogge, Christopher D.

Journal of the American Mathematical Society, Tome 06 (1993) no. 1, pp. 65-130

Détail

DOI : 10.1090/S0894-0347-1993-1168960-6

Bibliographie

[1] Beals, Richard Spatially inhomogeneous pseudodifferential operators. II Comm. Pure Appl. Math. 1974 161 205

[2] Bã©Rard, Pierre H. Riesz means of Riemannian manifolds 1980 1 12

[3] Besse, Arthur L. Manifolds all of whose geodesics are closed 1978

[4] Bourgain, J. Averages in the plane over convex curves and maximal operators J. Analyse Math. 1986 69 85

[5] Bourgain, J. Besicovitch type maximal operators and applications to Fourier analysis Geom. Funct. Anal. 1991 147 187

[6] Brenner, Philip 𝐿_{𝑝}-𝐿_{𝑝’}-estimates for Fourier integral operators related to hyperbolic equations Math. Z. 1977 273 286

[7] Carbery, Anthony The boundedness of the maximal Bochner-Riesz operator on 𝐿⁴(𝑅²) Duke Math. J. 1983 409 416

[8] Carbery, Anthony, Gasper, George, Trebels, Walter Radial Fourier multipliers of 𝐿^{𝑝}(𝑅²) Proc. Nat. Acad. Sci. U.S.A. 1984 3254 3255

[9] Carleson, Lennart, Sjã¶Lin, Per Oscillatory integrals and a multiplier problem for the disc Studia Math. 1972

[10] Christ, Michael On almost everywhere convergence of Bochner-Riesz means in higher dimensions Proc. Amer. Math. Soc. 1985 16 20

[11] Colin De Verdiã¨Re, Yves Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques Comment. Math. Helv. 1979 508 522

[12] Cã³Rdoba, A. A note on Bochner-Riesz operators Duke Math. J. 1979 505 511

[13] Cã³Rdoba, Antonio Geometric Fourier analysis Ann. Inst. Fourier (Grenoble) 1982

[14] Duistermaat, J. J., Guillemin, V. W. The spectrum of positive elliptic operators and periodic bicharacteristics Invent. Math. 1975 39 79

[15] Fefferman, Charles A note on spherical summation multipliers Israel J. Math. 1973 44 52

[16] Garcã­A-Cuerva, Josã©, Rubio De Francia, Josã© L. Weighted norm inequalities and related topics 1985

[17] Greenleaf, Allan, Uhlmann, Gunther Estimates for singular Radon transforms and pseudodifferential operators with singular symbols J. Funct. Anal. 1990 202 232

[18] Hã¶Rmander, Lars The spectral function of an elliptic operator Acta Math. 1968 193 218

[19] Hã¶Rmander, Lars Fourier integral operators. I Acta Math. 1971 79 183

[20] Journã©, J.-L., Soffer, A., Sogge, C. D. Decay estimates for Schrödinger operators Comm. Pure Appl. Math. 1991 573 604

[21] Kaneko, Makoto, Sunouchi, Gen-Ichirã´ On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions Tohoku Math. J. (2) 1985 343 365

[22] Mockenhaupt, Gerd, Seeger, Andreas, Sogge, Christopher D. Wave front sets, local smoothing and Bourgain’s circular maximal theorem Ann. of Math. (2) 1992 207 218

[23] Seeger, Andreas On quasiradial Fourier multipliers and their maximal functions J. Reine Angew. Math. 1986 61 73

[24] Seeger, A., Sogge, C. D. On the boundedness of functions of (pseudo-) differential operators on compact manifolds Duke Math. J. 1989 709 736

[25] Seeger, A., Sogge, C. D. Bounds for eigenfunctions of differential operators Indiana Univ. Math. J. 1989 669 682

[26] Seeger, Andreas, Sogge, Christopher D., Stein, Elias M. Regularity properties of Fourier integral operators Ann. of Math. (2) 1991 231 251

[27] Sogge, Christopher D. Oscillatory integrals and spherical harmonics Duke Math. J. 1986 43 65

[28] Sogge, Christopher D. Concerning the 𝐿^{𝑝} norm of spectral clusters for second-order elliptic operators on compact manifolds J. Funct. Anal. 1988 123 138

[29] Sogge, Christopher D. On the convergence of Riesz means on compact manifolds Ann. of Math. (2) 1987 439 447

[30] Sogge, Christopher D. Propagation of singularities and maximal functions in the plane Invent. Math. 1991 349 376

[31] Sogge, Christopher D., Stein, Elias M. Averages over hypersurfaces. II Invent. Math. 1986 233 242

[32] Sogge, C. D., Stein, E. M. Averages over hypersurfaces. Smoothness of generalized Radon transforms J. Analyse Math. 1990 165 188

[33] Stein, Elias M. Maximal functions. I. Spherical means Proc. Nat. Acad. Sci. U.S.A. 1976 2174 2175

[34] Stein, E. M. Oscillatory integrals in Fourier analysis 1986 307 355

[35] Sternberg, Shlomo Lectures on differential geometry 1964

[36] Strichartz, Robert S. A priori estimates for the wave equation and some applications J. Functional Analysis 1970 218 235

[37] Strichartz, Robert S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations Duke Math. J. 1977 705 714

[38] Weinstein, Alan Asymptotics of eigenvalue clusters for the Laplacian plus a potential Duke Math. J. 1977 883 892