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Volumn 225, Issue 4, 2010, Pages 1739-1785

Bilinear oscillatory integrals and boundedness for new bilinear multipliers

Author keywords

Bilinear multipliers; Oscillatory integrals

Indexed keywords


EID: 77956232653     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2010.03.032     Document Type: Article
Times cited : (25)

References (41)
  • 2
    • 72849147266 scopus 로고    scopus 로고
    • Uniform estimates for paraproducts and related multilinear operators
    • Bernicot Frédéric Uniform estimates for paraproducts and related multilinear operators. Rev. Mat. Iberoam. 2009, 25(3).
    • (2009) Rev. Mat. Iberoam. , vol.25 , Issue.3
    • Bernicot, F.1
  • 3
    • 77954174517 scopus 로고    scopus 로고
    • Local estimates and global continuities in Lebesgue spaces for non smooth bilinear operators
    • Bernicot Frédéric Local estimates and global continuities in Lebesgue spaces for non smooth bilinear operators. Anal. PDE 2008, 1:1-27.
    • (2008) Anal. PDE , vol.1 , pp. 1-27
    • Bernicot, F.1
  • 4
    • 77952422695 scopus 로고    scopus 로고
    • Use of abstract Hardy spaces, Real interpolation and applications to bilinear operators
    • Bernicot Frédéric Use of abstract Hardy spaces, Real interpolation and applications to bilinear operators. Math. Z. 2010, 265:365-400.
    • (2010) Math. Z. , vol.265 , pp. 365-400
    • Bernicot, F.1
  • 5
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
    • Bony Jean-Michel Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. Ecole Norm. Sup. 1981, 14:209-246.
    • (1981) Ann. Sci. Ecole Norm. Sup. , vol.14 , pp. 209-246
    • Bony, J.-M.1
  • 6
    • 29444457391 scopus 로고    scopus 로고
    • On multilinear oscillatory integrals, nonsingular and singular
    • Christ Michael, Li Xiaochun, Tao Terence, Thiele Christoph On multilinear oscillatory integrals, nonsingular and singular. Duke Math. J. 2005, 130(2):321-351.
    • (2005) Duke Math. J. , vol.130 , Issue.2 , pp. 321-351
    • Christ, M.1    Li, X.2    Tao, T.3    Thiele, C.4
  • 7
    • 84966238915 scopus 로고
    • On commutators of singular integrals and bilinear singular integrals
    • Coifman Ronald, Meyer Yves On commutators of singular integrals and bilinear singular integrals. Trans. Amer. Math. Soc. 1975, 212:315-331.
    • (1975) Trans. Amer. Math. Soc. , vol.212 , pp. 315-331
    • Coifman, R.1    Meyer, Y.2
  • 8
    • 0001923237 scopus 로고
    • Au delà des opérateurs pseudo-différentiels
    • Coifman Ronald, Meyer Yves Au delà des opérateurs pseudo-différentiels. Astérisque 1978, 57.
    • (1978) Astérisque , vol.57
    • Coifman, R.1    Meyer, Y.2
  • 9
    • 0001072134 scopus 로고
    • Commutateurs d'intégrales singulières et opérateurs multilinéaires
    • Coifman Ronald, Meyer Yves Commutateurs d'intégrales singulières et opérateurs multilinéaires. Ann. Inst. Fourier (Grenoble) 1978, 28:177-202.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , pp. 177-202
    • Coifman, R.1    Meyer, Y.2
  • 10
    • 84966261604 scopus 로고
    • Extensions of Hardy spaces and their use in analysis
    • Coifman Ronald, Weiss Guido Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 1977, 83:569-645.
    • (1977) Bull. Amer. Math. Soc. , vol.83 , pp. 569-645
    • Coifman, R.1    Weiss, G.2
  • 11
    • 0001720260 scopus 로고
    • A boundedness criterion for generalized Calderón Zygmund operators
    • David Guy, Journé Jean-Lin A boundedness criterion for generalized Calderón Zygmund operators. Ann. of Math. (2) 1984, 120(2):371-397.
    • (1984) Ann. of Math. (2) , vol.120 , Issue.2 , pp. 371-397
    • David, G.1    Journé, J.-L.2
  • 12
    • 0042229265 scopus 로고    scopus 로고
    • Bilinear space-time estimates for homogeneous wave equations
    • Foschi Damiano, Klainerman Sergiu Bilinear space-time estimates for homogeneous wave equations. Ann. Sci. École Norm. Sup. (4) 2000, 33(2):211-274.
    • (2000) Ann. Sci. École Norm. Sup. (4) , vol.33 , Issue.2 , pp. 211-274
    • Foschi, D.1    Klainerman, S.2
  • 13
    • 67650765274 scopus 로고    scopus 로고
    • Global solutions for 3D quadratic Schrödinger equations
    • Germain P., Masmoudi N., Shatah J. Global solutions for 3D quadratic Schrödinger equations. Int. Math. Res. Not. 2009, 3:414-432.
    • (2009) Int. Math. Res. Not. , vol.3 , pp. 414-432
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 15
    • 77956253718 scopus 로고    scopus 로고
    • Global solutions for 2D quadratic Schrödinger equations, preprint.
    • P. Germain, N. Masmoudi, J. Shatah, Global solutions for 2D quadratic Schrödinger equations, preprint.
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 16
    • 0034348694 scopus 로고    scopus 로고
    • Boundedness of bilinear operators with nonsmooth symbols
    • Gilbert John, Nahmod Andrea Boundedness of bilinear operators with nonsmooth symbols. Math. Res. Lett. 2000, 7:1-12.
    • (2000) Math. Res. Lett. , vol.7 , pp. 1-12
    • Gilbert, J.1    Nahmod, A.2
  • 17
    • 0000436415 scopus 로고    scopus 로고
    • Bilinear operators with nonsmooth symbols, Part I
    • Gilbert John, Nahmod Andrea Bilinear operators with nonsmooth symbols, Part I. J. Fourier Anal. Appl. 2000, 6(5):437-469.
    • (2000) J. Fourier Anal. Appl. , vol.6 , Issue.5 , pp. 437-469
    • Gilbert, J.1    Nahmod, A.2
  • 18
    • 0035998668 scopus 로고    scopus 로고
    • Bilinear operators with nonsmooth symbols, Part II
    • Gilbert John, Nahmod Andrea Bilinear operators with nonsmooth symbols, Part II. J. Fourier Anal. Appl. 2002, 8(2):109-172.
    • (2002) J. Fourier Anal. Appl. , vol.8 , Issue.2 , pp. 109-172
    • Gilbert, J.1    Nahmod, A.2
  • 19
    • 58149363006 scopus 로고
    • Generalized Strichartz inequalities for the wave equation
    • Ginibre Jean, Velo Giorgio Generalized Strichartz inequalities for the wave equation. J. Funct. Anal. 1995, 133(1):50-68.
    • (1995) J. Funct. Anal. , vol.133 , Issue.1 , pp. 50-68
    • Ginibre, J.1    Velo, G.2
  • 20
    • 0011572988 scopus 로고    scopus 로고
    • The Marcinkiewicz multiplier condition for bilinear operators
    • Grafakos Loukas, Kalton Nigel The Marcinkiewicz multiplier condition for bilinear operators. Stud. Math. 2001, 146(2):115-156.
    • (2001) Stud. Math. , vol.146 , Issue.2 , pp. 115-156
    • Grafakos, L.1    Kalton, N.2
  • 21
    • 33746725261 scopus 로고    scopus 로고
    • Interpolation of bilinear operators between quasi-Banach spaces
    • Grafakos Loukas, Mastylo Mieczyslaw Interpolation of bilinear operators between quasi-Banach spaces. Positivity 2006, 10(3):409-429.
    • (2006) Positivity , vol.10 , Issue.3 , pp. 409-429
    • Grafakos, L.1    Mastylo, M.2
  • 22
    • 33644558064 scopus 로고    scopus 로고
    • The disc as a bilinear multiplier
    • Grafakos Loukas, Li Xiaochun The disc as a bilinear multiplier. J. Amer. Math. Soc. 2006, 128(1):91-119.
    • (2006) J. Amer. Math. Soc. , vol.128 , Issue.1 , pp. 91-119
    • Grafakos, L.1    Li, X.2
  • 23
    • 84873059674 scopus 로고    scopus 로고
    • Bilinear Fourier integral operators, Journal of Pseudo-Differential Operators and Applications , submitted for publication.
    • Loukas Grafakos, Marco Peloso, Bilinear Fourier integral operators, Journal of Pseudo-Differential Operators and Applications (2010), submitted for publication.
    • (2010)
    • Grafakos, L.1    Peloso, M.2
  • 24
    • 0038367921 scopus 로고    scopus 로고
    • Multilinear interpolation between adjoint operators
    • Grafakos Loukas, Tao Terence Multilinear interpolation between adjoint operators. J. Funct. Anal. 2003, 199(2):379-385.
    • (2003) J. Funct. Anal. , vol.199 , Issue.2 , pp. 379-385
    • Grafakos, L.1    Tao, T.2
  • 25
    • 0037081869 scopus 로고    scopus 로고
    • Multilinear Calderón-Zygmund theory
    • Grafakos Loukas, Torres Rodolfo Multilinear Calderón-Zygmund theory. Adv. Math. 2002, 165(1):124-164.
    • (2002) Adv. Math. , vol.165 , Issue.1 , pp. 124-164
    • Grafakos, L.1    Torres, R.2
  • 26
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel Markus, Tao Terence Endpoint Strichartz estimates. Amer. J. Math. 1998, 120(5):955-980.
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 27
    • 0033243373 scopus 로고    scopus 로고
    • Multilinear estimates and fractional integration
    • Kenig Carlos, Stein Elias Multilinear estimates and fractional integration. Math. Res. Lett. 1999, 6(1):1-15.
    • (1999) Math. Res. Lett. , vol.6 , Issue.1 , pp. 1-15
    • Kenig, C.1    Stein, E.2
  • 28
    • 0000870142 scopus 로고
    • The null condition and global existence to nonlinear wave equations
    • Amer. Math. Soc., Providence, RI, Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1
    • Klainerman S. The null condition and global existence to nonlinear wave equations. Lectures in Appl. Math. 1986, vol. 23:293-326. Amer. Math. Soc., Providence, RI.
    • (1986) Lectures in Appl. Math. , vol.23 , pp. 293-326
    • Klainerman, S.1
  • 30
    • 0001283252 scopus 로고    scopus 로고
    • p estimates on the bilinear Hilbert transform for 2
    • p estimates on the bilinear Hilbert transform for 2
    • (1997) Ann. of Math. , vol.146 , pp. 693-724
    • Lacey, M.1    Thiele, C.2
  • 31
    • 0032574820 scopus 로고    scopus 로고
    • On the Calderón conjectures for the bilinear Hilbert transform
    • Lacey Mickael, Thiele Christoph On the Calderón conjectures for the bilinear Hilbert transform. Proc. Natl. Acad. Sci. USA 1998, 95:4828-4830.
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 4828-4830
    • Lacey, M.1    Thiele, C.2
  • 32
    • 0033416840 scopus 로고    scopus 로고
    • On Calderón's conjecture
    • Lacey Mickael, Thiele Christoph On Calderón's conjecture. Ann. of Math. 1999, 149:475-496.
    • (1999) Ann. of Math. , vol.149 , pp. 475-496
    • Lacey, M.1    Thiele, C.2
  • 33
    • 36248997661 scopus 로고    scopus 로고
    • Paraproducts with flag singularities I. A case study
    • Muscalu Camil Paraproducts with flag singularities I. A case study. Rev. Mat. Iberoam. 2007, 23:705-742.
    • (2007) Rev. Mat. Iberoam. , vol.23 , pp. 705-742
    • Muscalu, C.1
  • 35
    • 0036004363 scopus 로고    scopus 로고
    • Multi-linear operators given by singular multipliers
    • Muscalu Camil, Tao Terence, Thiele Christoph Multi-linear operators given by singular multipliers. J. Amer. Math. Soc. 2002, 15:469-496.
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 469-496
    • Muscalu, C.1    Tao, T.2    Thiele, C.3
  • 36
    • 0036942620 scopus 로고    scopus 로고
    • Uniforms estimates on multi-linear operators with modulation symmetry
    • Muscalu Camil, Tao Terence, Thiele Christoph Uniforms estimates on multi-linear operators with modulation symmetry. J. Anal. Math. 2002, 88:255-309.
    • (2002) J. Anal. Math. , vol.88 , pp. 255-309
    • Muscalu, C.1    Tao, T.2    Thiele, C.3
  • 37
    • 0035579785 scopus 로고    scopus 로고
    • Multilinear level set operators, oscillatory integral operators, and Newton polyhedra
    • Duong Hong Phong, Stein Elias, Sturm Jacob Multilinear level set operators, oscillatory integral operators, and Newton polyhedra. Math. Ann. 2001, 319(3):573-596.
    • (2001) Math. Ann. , vol.319 , Issue.3 , pp. 573-596
    • Duong Hong, P.1    Stein, E.2    Sturm, J.3
  • 38
    • 84990623722 scopus 로고
    • Normal forms and quadratic nonlinear Klein-Gordon equations
    • Shatah Jalal Normal forms and quadratic nonlinear Klein-Gordon equations. Comm. Pure Appl. Math. 1985, 38(5):685-696.
    • (1985) Comm. Pure Appl. Math. , vol.38 , Issue.5 , pp. 685-696
    • Shatah, J.1
  • 39
    • 0003300647 scopus 로고
    • Fourier Integrals in Classical Analysis
    • Cambridge University Press, Cambridge
    • Sogge Christopher Fourier Integrals in Classical Analysis. Cambridge Tracts in Math. 1993, vol. 105. Cambridge University Press, Cambridge.
    • (1993) Cambridge Tracts in Math. , vol.105
    • Sogge, C.1
  • 41
    • 84968497818 scopus 로고
    • Interpolation of operators with change of measures
    • Stein Elias, Weiss Guido Interpolation of operators with change of measures. Trans. Amer. Math. Soc. 1958, 87:159-172.
    • (1958) Trans. Amer. Math. Soc. , vol.87 , pp. 159-172
    • Stein, E.1    Weiss, G.2


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