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1999 | 132 | 2 | 125-139
Tytuł artykułu

On oscillatory integral operators with folding canonical relations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Sharp $L^p$ estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation $C_Φ$ projects to T*X and T*Y with fold singularities.
Czasopismo
Rocznik
Tom
132
Numer
2
Strony
125-139
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-04-11
Twórcy
  • Department of Mathematics, University of Wisconsin Madison, Wisconsin 53706, U.S.A., seeger@math.wisc.edu
Bibliografia
  • [1] J. Bourgain, Estimations de certaines fonctions maximales, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), 499-502.
  • [2] A. P. Calderón and R. Vaillancourt, A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185-1187.
  • [3] A. Carbery, A. Seeger, S. Wainger and J. Wright, Classes of singular integral operators along variable lines, J. Geom. Anal., to appear.
  • [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.
  • [5] A. Comech, Oscillatory integral operators in scattering theory, Comm. Partial Differential Equations 22 (1997), 841-867.
  • [6] S. Cuccagna, $L^2$ estimates for averaging operators along curves with two-sided k-fold singularities, Duke Math. J. 89 (1997), 203-216.
  • [7] A. Greenleaf and A. Seeger, Fourier integral operators with fold singularities, J. Reine Angew. Math. 455 (1994), 35-56.
  • [8] A. Greenleaf and A. Seeger, Fourier integral operators with simple cusps, Amer. J. Math., to appear.
  • [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.
  • [10] L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79-183.
  • [11] L. Hörmander, Oscillatory integrals and multipliers on $FL^p$, Ark. Mat. 11 (1973), 1-11.
  • [12] R. Melrose and M. Taylor, Near peak scattering and the correct Kirchhoff approximation for a convex obstacle, Adv. Math. 55 (1985), 242-315.
  • [13] Y. Pan, Hardy spaces and oscillatory integral operators, Rev. Mat. Iberoamericana 7 (1991), 55-64.
  • [14] Y. Pan, Hardy spaces and oscillatory integral operators, II, Pacific J. Math. 168 (1995), 167-182.
  • [15] Y. Pan and C. D. Sogge, Oscillatory integrals associated to folding canonical relations, Colloq. Math. 61 (1990), 413-419.
  • [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] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals and Radon transforms I, Acta Math. 157 (1986), 99-157.
  • [18] D. H. Phong and E. M. Stein, Radon transforms and torsion, Internat. Math. Res. Notices 4 (1991), 49-60.
  • [19] D. H. Phong and E. M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. 140 (1994), 703-722.
  • [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.
  • [21] A. Seeger, Degenerate Fourier integral operators in the plane, Duke Math. J. 71 (1993), 685-745.
  • [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.
  • [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] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.
  • [25] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv132i2p125bwm
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