Restriction theorems and maximal operators related to oscillatory integrals in $\mathbb{R}^3$
A. Moyua, A. Vargas, and L. Vega
Source: Duke Math. J. Volume 96, Number 3
(1999), 547-574.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077229325
Mathematical Reviews number (MathSciNet): MR1671214
Zentralblatt MATH identifier: 0946.42011
Digital Object Identifier: doi:10.1215/S0012-7094-99-09617-5
References
[BL] Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren Math. Wiss., vol. 223, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR58:2349
Zentralblatt MATH: 0344.46071
[B1] Jean Bourgain, On the restriction and multiplier problems in $\bf R\sp 3$, Geometric aspects of functional analysis (1989–90), Lecture Notes in Math., vol. 1469, Springer, Berlin, 1991, pp. 179–191.
Mathematical Reviews (MathSciNet): MR92m:42017
Zentralblatt MATH: 0792.42004
Digital Object Identifier: doi:10.1007/BFb0089225
[B2] J. Bourgain, A remark on Schrödinger operators, Israel J. Math. 77 (1992), no. 1-2, 1–16.
Mathematical Reviews (MathSciNet): MR93k:35071
Zentralblatt MATH: 0798.35131
Digital Object Identifier: doi:10.1007/BF02808007
[B3] J. Bourgain, Estimates for cone multipliers, Geometric aspects of functional analysis (Israel, 1992–1994), Oper. Theory Adv. Appl., vol. 77, Birkhäuser, Basel, 1995, pp. 41–60.
Mathematical Reviews (MathSciNet): MR96m:42022
Zentralblatt MATH: 0833.43008
[Cb] Anthony Carbery, Radial Fourier multipliers and associated maximal functions, Recent progress in Fourier analysis (El Escorial, 1983), North-Holland Math. Stud., vol. 111, North-Holland, Amsterdam, 1985, pp. 49–56.
Mathematical Reviews (MathSciNet): MR87i:42029
Zentralblatt MATH: 0632.42012
[C1] Lennart Carleson, Some analytic problems related to statistical mechanics, Euclidean harmonic analysis (Proc. Sem., Univ. Maryland, College Park, Md., 1979), Lecture Notes in Math., vol. 779, Springer, Berlin, 1980, pp. 5–45.
Mathematical Reviews (MathSciNet): MR82j:82005
Zentralblatt MATH: 0425.60091
[C1Sj] Lennart Carleson and Per Sjölin, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287–299. (errata insert).
Mathematical Reviews (MathSciNet): MR50:14052
Zentralblatt MATH: 0215.18303
[DK] Björn E. J. Dahlberg and Carlos E. Kenig, A note on the almost everywhere behavior of solutions to the Schrödinger equation, Harmonic analysis (Minneapolis, Minn., 1981), Lecture Notes in Math., vol. 908, Springer, Berlin, 1982, pp. 205–209.
Mathematical Reviews (MathSciNet): MR83f:35023
Zentralblatt MATH: 0519.35022
[F] Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36.
Mathematical Reviews (MathSciNet): MR41:2468
Zentralblatt MATH: 0188.42601
Digital Object Identifier: doi:10.1007/BF02394567
[KR] Carlos E. Kenig and Alberto Ruiz, A strong type $(2,\,2)$ estimate for a maximal operator associated to the Schrödinger equation, Trans. Amer. Math. Soc. 280 (1983), no. 1, 239–246.
Mathematical Reviews (MathSciNet): MR85c:42010
Zentralblatt MATH: 0525.42011
Digital Object Identifier: doi:10.2307/1999611
JSTOR: links.jstor.org
[MVV] A. Moyua, A. Vargas, and L. Vega, Schrödinger maximal function and restriction properties of the Fourier transform, Internat. Math. Res. Notices (1996), no. 16, 793–815.
Mathematical Reviews (MathSciNet): MR97k:42042
Zentralblatt MATH: 0868.35024
Digital Object Identifier: doi:10.1155/S1073792896000499
[PS] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1-2, 99–157.
Mathematical Reviews (MathSciNet): MR88i:42028a
Zentralblatt MATH: 0622.42011
Digital Object Identifier: doi:10.1007/BF02392592
[RV] Alberto Ruiz and Luis Vega, Corrigenda to: “Unique continuation for Schrödinger operators with potential in Morrey spaces”, Publ. Mat. 39 (1995), no. 2, 405–411.
Mathematical Reviews (MathSciNet): MR96m:35034
Zentralblatt MATH: 0849.47022
[Sj] Per Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), no. 3, 699–715.
Mathematical Reviews (MathSciNet): MR88j:35026
Zentralblatt MATH: 0631.42010
Digital Object Identifier: doi:10.1215/S0012-7094-87-05535-9
Project Euclid: euclid.dmj/1077306171
[St] Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993.
Mathematical Reviews (MathSciNet): MR95c:42002
Zentralblatt MATH: 0821.42001
[V] Luis Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), no. 4, 874–878.
Mathematical Reviews (MathSciNet): MR89d:35046
Zentralblatt MATH: 0654.42014
Digital Object Identifier: doi:10.2307/2047326
JSTOR: links.jstor.org
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