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On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity
Sobolev norm estimates for a class of bilinear multipliers
1. | Laboratoire Paul Painlevé - CNRS, Université Lille 1, 59655 Villeneuve d’Ascq Cedex |
2. | University of Zagreb, Department of Mathematics, Bijenička cesta 30, 10000 Zagreb, Croatia |
References:
[1] |
Á. Bényi, A. R. Nahmod and R. H. Torres, Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators, J. Geom. Anal., 16 (2006), 431-453.
doi: 10.1007/BF02922061. |
[2] |
Á. Bényi and R. H. Torres, Symbolic calculus and the transposes of bilinear pseudodifferential operators, Comm. Partial Differential Equations, 28 (2003), 1161-1181.
doi: 10.1081/PDE-120021190. |
[3] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-New York, 1976. Grundlehren der mathematischen Wissenschaften, 223. |
[4] |
F. Bernicot, A bilinear pseudodifferential calculus, J. Geom. Anal., 20 (2010), 39-62.
doi: 10.1007/s12220-009-9105-8. |
[5] |
F. Bernicot, Fiber-wise Calderón-Zygmund decomposition and application to a bi-dimensional paraproduct, Illinois J. Math., 56 (2012), 415-422. |
[6] |
R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Soc. Math. Fr., Paris, 1978. Astérisque, 57. |
[7] |
R. Coifman and Y. Meyer, Commutateurs d'intégrales singuliéres et opèrateurs multilinéaires, Ann. Inst. Fourier (Grenoble), 28 (1978), 177-202. |
[8] |
R. Coifman and Y. Meyer, Ondelettes et opérateurs. III. Opérateurs multilinéaires, Hermann, Paris, 1991. |
[9] |
C. Demeter and C. Thiele, On the two-dimensional bilinear Hilbert transform, Amer. J. Math., 132 (2010), 201-256.
doi: 10.1353/ajm.0.0101. |
[10] |
V. Kovač, Boundedness of the twisted paraproduct, Rev. Mat. Iberoam., 28 (2012), 1143-1164.
doi: 10.4171/RMI/707. |
[11] |
M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2 Ann. of Math., 146 (1997), 693-724.
doi: 10.2307/2952458. |
[12] |
M. Lacey and C. Thiele, On Calderón's conjecture, Ann. of Math., 149 (1999), 475-496.
doi: 10.2307/120971. |
[13] |
C. Muscalu, T. Tao and C. Thiele, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc., 15 (2002), 469-496.
doi: 10.1090/S0894-0347-01-00379-4. |
show all references
References:
[1] |
Á. Bényi, A. R. Nahmod and R. H. Torres, Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators, J. Geom. Anal., 16 (2006), 431-453.
doi: 10.1007/BF02922061. |
[2] |
Á. Bényi and R. H. Torres, Symbolic calculus and the transposes of bilinear pseudodifferential operators, Comm. Partial Differential Equations, 28 (2003), 1161-1181.
doi: 10.1081/PDE-120021190. |
[3] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-New York, 1976. Grundlehren der mathematischen Wissenschaften, 223. |
[4] |
F. Bernicot, A bilinear pseudodifferential calculus, J. Geom. Anal., 20 (2010), 39-62.
doi: 10.1007/s12220-009-9105-8. |
[5] |
F. Bernicot, Fiber-wise Calderón-Zygmund decomposition and application to a bi-dimensional paraproduct, Illinois J. Math., 56 (2012), 415-422. |
[6] |
R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Soc. Math. Fr., Paris, 1978. Astérisque, 57. |
[7] |
R. Coifman and Y. Meyer, Commutateurs d'intégrales singuliéres et opèrateurs multilinéaires, Ann. Inst. Fourier (Grenoble), 28 (1978), 177-202. |
[8] |
R. Coifman and Y. Meyer, Ondelettes et opérateurs. III. Opérateurs multilinéaires, Hermann, Paris, 1991. |
[9] |
C. Demeter and C. Thiele, On the two-dimensional bilinear Hilbert transform, Amer. J. Math., 132 (2010), 201-256.
doi: 10.1353/ajm.0.0101. |
[10] |
V. Kovač, Boundedness of the twisted paraproduct, Rev. Mat. Iberoam., 28 (2012), 1143-1164.
doi: 10.4171/RMI/707. |
[11] |
M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2 Ann. of Math., 146 (1997), 693-724.
doi: 10.2307/2952458. |
[12] |
M. Lacey and C. Thiele, On Calderón's conjecture, Ann. of Math., 149 (1999), 475-496.
doi: 10.2307/120971. |
[13] |
C. Muscalu, T. Tao and C. Thiele, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc., 15 (2002), 469-496.
doi: 10.1090/S0894-0347-01-00379-4. |
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