In this paper, we discuss decay estimates and Strichartz estimates for dispersive equations with non-homogeneous symbols on modulation spaces M-p,q(s) to obtain the global well-posedness of the Cauchy problems for non...
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In this paper, we discuss decay estimates and Strichartz estimates for dispersive equations with non-homogeneous symbols on modulation spaces M-p,q(s) to obtain the global well-posedness of the Cauchy problems for nonlinear dispersive equations. As a result, we have a generalization of the result in [19] which treated the Schrodinger equations with a nonlinearity of wider class. (C) 2013 Elsevier Inc. All rights reserved.
We prove global wellposedness of the Klein-Gordon equation with power nonlinearity vertical bar u vertical bar(alpha-1)u, where alpha epsilon [1, d/d-2], in dimension d >= 3 with initial data in M-p,p'(1) (R-d)...
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We prove global wellposedness of the Klein-Gordon equation with power nonlinearity vertical bar u vertical bar(alpha-1)u, where alpha epsilon [1, d/d-2], in dimension d >= 3 with initial data in M-p,p'(1) (R-d) x M-p,M-p' (R-d) for p sufficiently close to 2. The proof is an application of the high-low method described by Bourgain in [Global solutions of nonlinear Schrodinger equations, American Mathematical Society, Providence, RI, 1999] where the Klein-Gordon equation is studied in one dimension with cubic nonlinearity for initial data in Sobolev spaces.
We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schrodinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are prov...
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We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schrodinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved quantities based on the complete integrability of the equation, persistence of regularity, and by separating off the time evolution of finitely many Picard iterates.
In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
In this paper, we mainly study the boundedness of unimodular Fourier multipliers with a time parameter e(itp(xi)) on the modulation spaces where p(xi) is a differentiable real-valued function, namely we estimate e(itp...
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In this paper, we mainly study the boundedness of unimodular Fourier multipliers with a time parameter e(itp(xi)) on the modulation spaces where p(xi) is a differentiable real-valued function, namely we estimate e(itp(xi)) under the multiplier norm, denoted by M-s,M-p. The sharpness of s and the regularity lost are also discussed when the multiplier acts on functions in modulation spaces. Meanwhile the lower bound of the multiplier is shown. Finally, we present a discussion of the relationship between the main result and well-posedness results for nonlinear PDEs already existing in the literature.
We study the continuity on the modulation spaces M-p,M-q of Fourier multipliers with symbols of the type e(i mu(xi)), for some real-valued function mu(xi). A number of results are known, assuming that the derivatives ...
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We study the continuity on the modulation spaces M-p,M-q of Fourier multipliers with symbols of the type e(i mu(xi)), for some real-valued function mu(xi). A number of results are known, assuming that the derivatives of order >= 2 of the phase mu(xi) are bounded or, more generally, that the second derivatives belong to the Sjostrand class M-infinity,M- 1. Here we extend those results, by assuming that the second derivatives lie in the bigger Wiener amalgam space W(FL1,L-infinity);in particular they could have stronger oscillations at infinity such as cos vertical bar xi vertical bar(2). Actually our main result deals with the more general case of possibly unbounded second derivatives. In that case we have boundedness on weighted modulation spaces with a sharp loss of derivatives.
We establish both a local and a global well-posedness theories for the nonlinear Hartree-Fock equations and its reduced analog in the setting of the modulation spaces on In addition, we prove similar results when a ha...
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We establish both a local and a global well-posedness theories for the nonlinear Hartree-Fock equations and its reduced analog in the setting of the modulation spaces on In addition, we prove similar results when a harmonic potential is added to the equations. In the process, we prove the boundedeness of certain multilinear operators on products of the modulation spaces which may be of independent interest.
We prove sharp estimates for the dilation operator f(x) bar right arrow f(lambda x), when acting on Wiener amalgam spaces W(L-p, L-q). Scaling arguments are also used to prove the sharpness of the known convolution an...
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We prove sharp estimates for the dilation operator f(x) bar right arrow f(lambda x), when acting on Wiener amalgam spaces W(L-p, L-q). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces M-p,M-q, as well as the optimality of an estimate for the Schrodinger propagator on modulation spaces.
In this paper, we establish the Cowling-Price's, Hardy's and Morgan's uncertainty principles for the Opdam-Cherednik transform on modulation spaces associated with this transform. The proofs of the theorem...
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In this paper, we establish the Cowling-Price's, Hardy's and Morgan's uncertainty principles for the Opdam-Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi-Cherednik operator and the versions of the Phragmen-Lindlof type result for the modulation spaces.
The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on R-n circle plus R-n. In this paper we will show that the replacement of this structure by an arbitrary symplecti...
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The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on R-n circle plus R-n. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on R-n but rather on R-n circle plus R-n. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometrics of L-2(R-n) -> L-2(R-2n) indexed by S(R-n). This allows us to obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces. (C) 2011 Elsevier Masson SAS. All rights reserved.
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