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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,, \emph{J. Geom. Anal.}, 16 (2006), 431.
doi: 10.1007/BF02922061. |
[2] |
Á. Bényi and R. H. Torres, Symbolic calculus and the transposes of bilinear pseudodifferential operators,, \emph{Comm. Partial Differential Equations}, 28 (2003), 1161.
doi: 10.1081/PDE-120021190. |
[3] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction,, Springer-Verlag, 223 (1976).
|
[4] |
F. Bernicot, A bilinear pseudodifferential calculus,, \emph{J. Geom. Anal.}, 20 (2010), 39.
doi: 10.1007/s12220-009-9105-8. |
[5] |
F. Bernicot, Fiber-wise Calderón-Zygmund decomposition and application to a bi-dimensional paraproduct,, \emph{Illinois J. Math.}, 56 (2012), 415. Google Scholar |
[6] |
R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels,, Soc. Math. Fr., 57 (1978).
|
[7] |
R. Coifman and Y. Meyer, Commutateurs d'intégrales singuliéres et opèrateurs multilinéaires,, \emph{Ann. Inst. Fourier} (Grenoble), 28 (1978), 177.
|
[8] |
R. Coifman and Y. Meyer, Ondelettes et opérateurs. III. Opérateurs multilinéaires,, Hermann, (1991).
|
[9] |
C. Demeter and C. Thiele, On the two-dimensional bilinear Hilbert transform,, \emph{Amer. J. Math.}, 132 (2010), 201.
doi: 10.1353/ajm.0.0101. |
[10] |
V. Kovač, Boundedness of the twisted paraproduct,, \emph{Rev. Mat. Iberoam.}, 28 (2012), 1143.
doi: 10.4171/RMI/707. |
[11] |
M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2 \emph{Ann. of Math.}, 146 (1997), 693.
doi: 10.2307/2952458. |
[12] |
M. Lacey and C. Thiele, On Calderón's conjecture,, \emph{Ann. of Math.}, 149 (1999), 475.
doi: 10.2307/120971. |
[13] |
C. Muscalu, T. Tao and C. Thiele, Multi-linear operators given by singular multipliers,, \emph{J. Amer. Math. Soc.}, 15 (2002), 469.
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,, \emph{J. Geom. Anal.}, 16 (2006), 431.
doi: 10.1007/BF02922061. |
[2] |
Á. Bényi and R. H. Torres, Symbolic calculus and the transposes of bilinear pseudodifferential operators,, \emph{Comm. Partial Differential Equations}, 28 (2003), 1161.
doi: 10.1081/PDE-120021190. |
[3] |
J. Bergh and J. Löfström, Interpolation Spaces. An Introduction,, Springer-Verlag, 223 (1976).
|
[4] |
F. Bernicot, A bilinear pseudodifferential calculus,, \emph{J. Geom. Anal.}, 20 (2010), 39.
doi: 10.1007/s12220-009-9105-8. |
[5] |
F. Bernicot, Fiber-wise Calderón-Zygmund decomposition and application to a bi-dimensional paraproduct,, \emph{Illinois J. Math.}, 56 (2012), 415. Google Scholar |
[6] |
R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels,, Soc. Math. Fr., 57 (1978).
|
[7] |
R. Coifman and Y. Meyer, Commutateurs d'intégrales singuliéres et opèrateurs multilinéaires,, \emph{Ann. Inst. Fourier} (Grenoble), 28 (1978), 177.
|
[8] |
R. Coifman and Y. Meyer, Ondelettes et opérateurs. III. Opérateurs multilinéaires,, Hermann, (1991).
|
[9] |
C. Demeter and C. Thiele, On the two-dimensional bilinear Hilbert transform,, \emph{Amer. J. Math.}, 132 (2010), 201.
doi: 10.1353/ajm.0.0101. |
[10] |
V. Kovač, Boundedness of the twisted paraproduct,, \emph{Rev. Mat. Iberoam.}, 28 (2012), 1143.
doi: 10.4171/RMI/707. |
[11] |
M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2 \emph{Ann. of Math.}, 146 (1997), 693.
doi: 10.2307/2952458. |
[12] |
M. Lacey and C. Thiele, On Calderón's conjecture,, \emph{Ann. of Math.}, 149 (1999), 475.
doi: 10.2307/120971. |
[13] |
C. Muscalu, T. Tao and C. Thiele, Multi-linear operators given by singular multipliers,, \emph{J. Amer. Math. Soc.}, 15 (2002), 469.
doi: 10.1090/S0894-0347-01-00379-4. |
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