Pointwise estimates for a class of oscillatory integrals and related \(L^p\)--\(L^q\) estimates

DOI10.1007/s00041-005-4067-0zbMath1089.42011OpenAlexW186143042MaRDI QIDQ818505

Shang-bin Cui

Publication date: 21 March 2006

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-005-4067-0

zbMATH Keywords

dispersive equationoscillatory integral\(L^p\)--\(L^q\)-estimate

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Maximal functions, Littlewood-Paley theory (42B25) Multipliers in one variable harmonic analysis (42A45) Fourier integral operators applied to PDEs (35S30)

Related Items (12)

Well-posedness of Cauchy problem of fourth-order Schrödinger equations in anisotropic Sobolev space ⋮ On the Cauchy problem of fourth-order nonlinear Schrödinger equations ⋮ Well-posedness of higher-order nonlinear Schrödinger equations in Sobolev spaces \(H^{s}(\mathbb R^{n})\) and applications ⋮ Estimates for a class of oscillatory integrals and decay rates for wave-type equations ⋮ \(L^p\)-\(L^q\) estimates for a class of pseudo-differential equations and their applications ⋮ Dispersive Estimates with Geometry of Finite Type ⋮ Solvability of the Cauchy problem of non-isotropic Schrödinger equations in Sobolev spaces ⋮ Global estimates of fundamental solutions for higher-order Schrödinger equations ⋮ Well-posedness of the fourth-order perturbed Schrödinger type equation in non-isotropic Sobolev spaces ⋮ Well-posedness of the Cauchy problem of high dimension non-isotropic fourth-order Schrödinger equations in Sobolev spaces ⋮ \(L^p-L^q\) estimates for dispersive equations and related applications ⋮ Cauchy problem for higher-order Schrödinger equations in anisotropic Sobolev space

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