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Volumn 13, Issue 6, 2003, Pages 1359-1384

A sharp bilinear restriction estimate for paraboloids

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EID: 1142264310     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-003-0449-0     Document Type: Article
Times cited : (316)

References (29)
  • 1
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for lattice subsets and applications to nonlinear evolution equations I, II
    • [B1], GAFA
    • [B1] J. BOURGAIN, Fourier transform restriction phenomena for lattice subsets and applications to nonlinear evolution equations I, II, GAFA, Geom. funct. anal. 3 (1993), 107-156, 209-262.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 2
    • 51249164767 scopus 로고
    • A remark on Schrodinger operators
    • [B2]
    • [B2] J. BOURGAIN, A remark on Schrodinger operators, Israel J. Math. 77 (1992), 1-16.
    • (1992) Israel J. Math. , vol.77 , pp. 1-16
    • Bourgain, J.1
  • 3
    • 0002447866 scopus 로고
    • Some new estimates on oscillatory integrals
    • [B3], Princeton University Press
    • [B3] J. BOURGAIN, Some new estimates on oscillatory integrals, Essays in Fourier Analysis in honor of E.M. Stein, Princeton University Press (1995), 83-112.
    • (1995) Essays in Fourier Analysis in Honor of E.M. Stein , pp. 83-112
    • Bourgain, J.1
  • 5
    • 0347803639 scopus 로고    scopus 로고
    • Harmonic analysis and combinatorics: How much may they contribute to each other?
    • [B5], IMU/Amer. Math. Society
    • [B5] J. BOURGAIN, Harmonic analysis and combinatorics: How much may they contribute to each other?, Mathematics: Frontiers and perspectives, IMU/Amer. Math. Society (2000), 13-32.
    • (2000) Mathematics: Frontiers and Perspectives , pp. 13-32
    • Bourgain, J.1
  • 6
    • 0040561692 scopus 로고
    • Restriction implies Bochner-Riesz for paraboloids
    • [C]
    • [C] A. CARBERY, Restriction implies Bochner-Riesz for paraboloids, Math. Proc. Cambridge Philos. Soc. 111:3 (1992), 525-529.
    • (1992) Math. Proc. Cambridge Philos. Soc. , vol.111 , Issue.3 , pp. 525-529
    • Carbery, A.1
  • 7
    • 0010954950 scopus 로고
    • Inequalities for strongly singular convolution operators
    • [F]
    • [F] C. FEFFERMAN, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36.
    • (1970) Acta Math. , vol.124 , pp. 9-36
    • Fefferman, C.1
  • 9
    • 84990576528 scopus 로고
    • Space-time Estimates for null forms and the local existence theorem
    • [KM]
    • [KM] S. KLAINERMAN, M. MACHEDON, Space-time Estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 1221-1268.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 1221-1268
    • Klainerman, S.1    Machedon, M.2
  • 10
    • 0036435173 scopus 로고    scopus 로고
    • A physical space approach to wave equation bilinear estimates
    • [KRT]
    • [KRT] S. KLAINERMAN, I. RODNIANSKI, T. TAO, A physical space approach to wave equation bilinear estimates, J. Anal. Math. 87 (2002), 299-336.
    • (2002) J. Anal. Math. , vol.87 , pp. 299-336
    • Klainerman, S.1    Rodnianski, I.2    Tao, T.3
  • 11
    • 84966250322 scopus 로고
    • A note on the cone multiplier
    • [M]
    • [M] G. MOCKENHAUPT, A note on the cone multiplier, Proc. AMS 117 (1993), 145-152.
    • (1993) Proc. AMS , vol.117 , pp. 145-152
    • Mockenhaupt, G.1
  • 12
    • 1842431121 scopus 로고    scopus 로고
    • Schrödinger maximal function and restriction properties of the Fourier transform
    • [MoVV1]
    • [MoVV1] A. MOYUA, A. VARGAS, L. VEGA, Schrödinger maximal function and restriction properties of the Fourier transform, International Math. Research Notices 16 (1996), 793-815.
    • (1996) International Math. Research Notices , vol.16 , pp. 793-815
    • Moyua, A.1    Vargas, A.2    Vega, L.3
  • 14
    • 0036350601 scopus 로고    scopus 로고
    • Dispersive estimates the 2d cubic Nls equation
    • [P]
    • [P] F. PLANCHON, Dispersive estimates and the 2D cubic NLS equation, Journal d'Analyse Mathématiques 86 (2002), 319-334.
    • (2002) Journal d'Analyse Mathématiques , vol.86 , pp. 319-334
    • Planchon, F.1
  • 15
    • 0001679726 scopus 로고
    • Regularity of solutions to Schrödinger equations
    • [S]
    • [S] P. SJÖLIN, Regularity of solutions to Schrödinger equations, Duke Math. J. 55 (1987), 699-715.
    • (1987) Duke Math. J. , vol.55 , pp. 699-715
    • Sjölin, P.1
  • 16
    • 0010041335 scopus 로고    scopus 로고
    • Some problems in harmonic analysis, Harmonic analysis in Euclidean spaces
    • [St1], Williams Coll., Williamstown, Mass., 1978
    • [St1] E.M. STEIN, Some problems in harmonic analysis, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1 (1997), 3-20.
    • (1997) Proc. Sympos. Pure Math. , Issue.PART 1 , pp. 3-20
    • Stein, E.M.1
  • 17
    • 0004136765 scopus 로고
    • [St2], Princeton University Press
    • [St2] E.M. STEIN, Harmonic Analysis, Princeton University Press, 1993.
    • (1993) Harmonic Analysis
    • Stein, E.M.1
  • 18
    • 84972553620 scopus 로고
    • Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations
    • [Str]
    • [Str] R. S. STRICHARTZ, Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-774.
    • (1977) Duke Math. J. , vol.44 , pp. 705-774
    • Strichartz, R.S.1
  • 19
    • 0002623032 scopus 로고    scopus 로고
    • From rotating needles to stability of waves: Emerging connections between combinatorics, analysis, and PDE
    • [T1]
    • [T1] T. TAO, From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE, Notices Amer. Math. Soc. 48 (2001), 294-303.
    • (2001) Notices Amer. Math. Soc. , vol.48 , pp. 294-303
    • Tao, T.1
  • 21
    • 0035621582 scopus 로고    scopus 로고
    • Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates
    • [T3]
    • [T3] T. TAO, Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates, Math Z. 238 (2001), 215-268.
    • (2001) Math Z. , vol.238 , pp. 215-268
    • Tao, T.1
  • 22
    • 0034384186 scopus 로고    scopus 로고
    • A bilinear approach to cone multipliers I. Restriction Estimates
    • [TV1], GAFA
    • [TV1] T. TAO, A. VARGAS, A bilinear approach to cone multipliers I. Restriction Estimates, GAFA, Geom. funct. anal. 10 (2000), 185-215.
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 185-215
    • Tao, T.1    Vargas, A.2
  • 23
    • 0034403909 scopus 로고    scopus 로고
    • A bilinear approach to cone multipliers II. Applications
    • [TV2], GAFA
    • [TV2] T. TAO, A. VARGAS, A bilinear approach to cone multipliers II. Applications, GAFA, Geom. funct. anal. 10 (2000), 216-258.
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 216-258
    • Tao, T.1    Vargas, A.2
  • 24
    • 0032343059 scopus 로고    scopus 로고
    • A bilinear approach to the restriction and Kakeya conjectures
    • [TVV]
    • [TVV] T. TAO, A. VARGAS, L. VEGA, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998). 967-1000.
    • (1998) J. Amer. Math. Soc. , vol.11 , pp. 967-1000
    • Tao, T.1    Vargas, A.2    Vega, L.3
  • 26
    • 21844498188 scopus 로고
    • An improved bound for Kakeya type maximal functions
    • [W1]
    • [W1] T. WOLFF, An improved bound for Kakeya type maximal functions, Revista Mat. Iberoamericana 11 (1995). 651-674.
    • (1995) Revista Mat. Iberoamericana , vol.11 , pp. 651-674
    • Wolff, T.1
  • 27
    • 0002849466 scopus 로고    scopus 로고
    • Recent work connected with the Kakeya problem
    • [W2] (Princeton, NJ, 1996), Amer. Math. Soc., Providence, RI
    • [W2] T. WOLFF, Recent work connected with the Kakeya problem, Prospects in Mathematics (Princeton, NJ, 1996), Amer. Math. Soc., Providence, RI (1999), 129-162.
    • (1999) Prospects in Mathematics , pp. 129-162
    • Wolff, T.1
  • 28
    • 0035532958 scopus 로고    scopus 로고
    • A sharp bilinear cone restriction estimate
    • [W3]
    • [W3] T. WOLFF, A sharp bilinear cone restriction estimate, Annals of Math. (2) 153:3 (2001), 661-698.
    • (2001) Annals of Math. (2) , vol.153 , Issue.3 , pp. 661-698
    • Wolff, T.1
  • 29
    • 23044524808 scopus 로고    scopus 로고
    • p for large p
    • [W4], GAFA
    • p for large p, GAFA, Geom. funct. anal. 10:5 (2000), 1237-1288.
    • (2000) Geom. Funct. Anal. , vol.10 , Issue.5 , pp. 1237-1288
    • Wolff, T.1


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