메뉴 건너뛰기




Volumn 25, Issue 3, 2009, Pages 1127-1168

Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case

Author keywords

Cylindrical symmetry; Restriction conjecture; Schr dinger equation

Indexed keywords


EID: 72849123518     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/591     Document Type: Article
Times cited : (33)

References (29)
  • 1
    • 0000420259 scopus 로고
    • Besicovitch type maximal operators and applications to Fourier analysis
    • BOURGAIN, J.: Besicovitch type maximal operators and applications to Fourier analysis. Geom. Funct. Anal. 1 (1991), no.2, 147-187.
    • (1991) Geom. Funct. Anal. , vol.1 , Issue.2 , pp. 147-187
    • Bourgain, J.1
  • 2
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations
    • BOURGAIN, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3 (1993), no.2, 107-156.
    • (1993) Geom. Funct. Anal. , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 3
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. H. the KdVequation
    • BOURGAIN, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. H. The KdVequation. Geom. Funct. Anal. 3 (1993), no.3, 209-262.
    • (1993) Geom. Funct. Anal. , vol.3 , Issue.3 , pp. 209-262
    • Bourgain, J.1
  • 4
    • 85157050102 scopus 로고    scopus 로고
    • American Mathematical Society Colloquium Publications American Mathematical Society, Providence, RI
    • BOURGAIN, J.: Global solutions of nonlinear Schrödinger equations. American Mathematical Society Colloquium Publications 46. American Mathematical Society, Providence, RI, 1999.
    • (1999) Global Solutions of Nonlinear Schrödinger Equations , vol.46
    • Bourgain, J.1
  • 5
    • 0000692012 scopus 로고
    • Oscillatory integrals and a multiplier problem for the disc
    • errata insert
    • CARLESON, L. AND SJÖLIN, P.: Oscillatory integrals and a multiplier problem for the disc. Studia Math. 44 (1972), 287-299. (errata insert).
    • (1972) Studia Math. , vol.44 , pp. 287-299
    • Carleson, L.1    Sjölin, P.2
  • 6
    • 0001947077 scopus 로고
    • The Kakeya maximal function and the spherical summation multipliers
    • CORDOBA, A.: The Kakeya maximal function and the spherical summation multipliers. Amer. J. Math. 99 (1977), no.1, 1-22.
    • (1977) Amer. J. Math. , vol.99 , Issue.1 , pp. 1-22
    • Cordoba, A.1
  • 7
    • 0000361611 scopus 로고
    • Some maximal inequalities
    • FEFFERMAN, C AND STEIN, E. M.: Some maximal inequalities. Amer. J. Math. 93 (1971), 107-115.
    • (1971) Amer. J. Math. , vol.93 , pp. 107-115
    • Fefferman, C.1    Stein, E.M.2
  • 8
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • KEEL, M. AND TAO, T.: Endpoint Strichartz estimates. Amer. J. Math. 120 (1998), no.5, 955-980.
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 9
    • 84990576528 scopus 로고
    • Space-time estimates for null forms and the local existence theorem
    • KLAINERMAN, S. AND MACHEDON, M.: Space-time estimates for null forms and the local existence theorem. Comm. Pure Appl. Math. 46 (1993), no.9, 1221-1268.
    • (1993) Comm. Pure Appl. Math. , vol.46 , Issue.9 , pp. 1221-1268
    • Klainerman, S.1    Machedon, M.2
  • 10
    • 54349117254 scopus 로고    scopus 로고
    • Sharp null forms estimates for the wave equation
    • LEE, S. AND VARGAS, A.: Sharp null forms estimates for the wave equation. Amer. J. Math. 130 (2008), no.5, 1279-1326.
    • (2008) Amer. J. Math. , vol.130 , Issue.5 , pp. 1279-1326
    • Lee, S.1    Vargas, A.2
  • 11
    • 1842431121 scopus 로고    scopus 로고
    • Schrödinger maximal function and restriction properties of the Fourier transform
    • MOYUA, A., VARGAS, A. AND VEGA, L.: Schrödinger maximal function and restriction properties of the Fourier transform. Internat. Math. Res. Notices (1996), no.16, 793-815.
    • (1996) Internat. Math. Res. Notices , Issue.16 , pp. 793-815
    • Moyua, A.1    Vargas, A.2    Vega, L.3
  • 14
    • 0003552286 scopus 로고
    • Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals
    • Princeton University Press, Princeton, NJ
    • STEIN, E. M.: Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series 43. Princeton University Press, Princeton, NJ, 1993.
    • (1993) Princeton Mathematical Series , vol.43
    • Stein, E.M.1
  • 15
    • 0003517185 scopus 로고
    • Introduction to Fourier analysis on Euclidean spaces
    • Princeton University Press, Princeton, NJ
    • STEIN, E. M. AND WEISS, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series 32. Princeton University Press, Princeton, NJ, 1971.
    • (1971) Princeton Mathematical Series , vol.32
    • Stein, E.M.1    Weiss, G.2
  • 16
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • STRICHARTZ, R. S.: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Dulce Math. J. 44 (1977), no.3, 705-714.
    • (1977) Dulce Math. J. , vol.44 , Issue.3 , pp. 705-714
    • Strichartz, R.S.1
  • 17
    • 72849113254 scopus 로고    scopus 로고
    • Recent progress on the restriction conjecture
    • In Fourier analysis and convexity. Birkhäuser Boston, Boston, MA
    • TAO, T.: Recent progress on the restriction conjecture. In Fourier analysis and convexity, 217-243. Appl. Numer. Harmon. Anal. Birkhäuser Boston, Boston, MA, 2004.
    • (2004) Appl. Numer. Harmon. Anal , pp. 217-243
    • Tao, T.1
  • 18
    • 0001380081 scopus 로고    scopus 로고
    • The Bochner-Riesz conjecture implies the restriction conjecture
    • TAO, T.: The Bochner-Riesz conjecture implies the restriction conjecture. Duke Math. J. 96 (1999), no.2, 363-375.
    • (1999) Duke Math. J. , vol.96 , Issue.2 , pp. 363-375
    • Tao, T.1
  • 19
    • 0035621582 scopus 로고    scopus 로고
    • Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates
    • TAO, T.: Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates. Math. Z. 238 (2001), no.2, 215-268.
    • (2001) Math. Z. , vol.238 , Issue.2 , pp. 215-268
    • Tao, T.1
  • 20
    • 1142264310 scopus 로고    scopus 로고
    • A sharp bilinear restrictions estimate for paraboloids
    • TAO, T.: A sharp bilinear restrictions estimate for paraboloids. Geom. Funct. Anal. 13 (2003), no.6, 1359-1384.
    • (2003) Geom. Funct. Anal. , vol.13 , Issue.6 , pp. 1359-1384
    • Tao, T.1
  • 21
    • 33845293767 scopus 로고    scopus 로고
    • A counterexample to an endpoint bilinear Strichartz inequality
    • electronic
    • TAO, T.: A counterexample to an endpoint bilinear Strichartz inequality. Electron. J. Differential Equations (2006), no.151, 6 pp. (electronic)
    • (2006) Electron. J. Differential Equations , Issue.151
    • Tao, T.1
  • 22
    • 0034403909 scopus 로고    scopus 로고
    • A bilinear approach to cone multipliers. II. Applications
    • TAO, T. AND VARGAS, A.: A bilinear approach to cone multipliers. II. Applications. Geom. Funct. Anal. 10 (2000), no.1, 216-258.
    • (2000) Geom. Funct. Anal. , vol.10 , Issue.1 , pp. 216-258
    • Tao, T.1    Vargas, A.2
  • 23
    • 0032343059 scopus 로고    scopus 로고
    • A bilinear approach to the restriction and Kakeya conjectures
    • TAO, T., VARGAS, A. AND VEGA, L.: A bilinear approach to the restriction and Kakeya conjectures. J. Amer. Math. Soc. 11 (1998), no.4, 967-1000. (Pubitemid 128140132)
    • (1998) Journal of the American Mathematical Society , vol.11 , Issue.4 , pp. 967-1000
    • Tao, T.1    Vargas, A.2    Vega, L.3
  • 24
    • 35349001167 scopus 로고    scopus 로고
    • Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
    • TAO, T., VISAN, M. AND ZHANG, X.: Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. Duke Math. J. 140 (2007), no.1, 165-202.
    • (2007) Duke Math. J. , vol.140 , Issue.1 , pp. 165-202
    • Tao, T.1    Visan, M.2    Zhang, X.3
  • 25
    • 84968496791 scopus 로고
    • A restriction theorem for the Fourier transform
    • TOMAS, P. A.: A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc. 81 (1975), 477-478.
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 477-478
    • Tomas, P.A.1
  • 26
    • 0035379526 scopus 로고    scopus 로고
    • Regularity of solutions to the free Schrödinger equation with radial initial data
    • VILELA, M. C: Regularity of solutions to the free Schrödinger equation with radial initial data. Illinois J. Math. 45 (2001), no.2, 361-370. (Pubitemid 33571865)
    • (2001) Illinois Journal of Mathematics , vol.45 , Issue.2 , pp. 361-370
    • Vilela, M.C.1
  • 27
    • 21844498188 scopus 로고
    • An improved bound for Kakeya type maximal functions
    • WOLFF, T.: An improved bound for Kakeya type maximal functions. Rev. Mat. Iberoamericana 11 (1995), no.3, 651-674.
    • (1995) Rev. Mat. Iberoamericana , vol.11 , Issue.3 , pp. 651-674
    • Wolff, T.1
  • 28
    • 0035532958 scopus 로고    scopus 로고
    • A sharp bilinear cone restriction estimate
    • WOLFF, T.: A sharp bilinear cone restriction estimate. Ann. of Math. (2) 153 (2001), no.3, 661-698.
    • (2001) Ann. of Math. (2) , vol.153 , Issue.3 , pp. 661-698
    • Wolff, T.1
  • 29
    • 0000855641 scopus 로고
    • On Fourier coefficients and transforms of functions of two variables
    • ZYGMUND, A.: On Fourier coefficients and transforms of functions of two variables. Studia Math. 50 (1974), 189-201.
    • (1974) Studia Math. , vol.50 , pp. 189-201
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.