Convex hypersurfaces and \(L^p\) estimates for Schrödinger equations.

DOI10.1016/S0022-1236(03)00144-7zbMath1161.35474arXivmath/0403321OpenAlexW2084510391MaRDI QIDQ1428453

Quan Zheng, Fan, Dashan, Xiao Hua Yao

Publication date: 29 March 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403321

zbMATH Keywords

Schrödinger equation\(L^p\) estimateConvex hypersurfaceFinite typeIntegrated group

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) PDEs in connection with quantum mechanics (35Q40) Integrated semigroups (47D62)

Related Items

Unique continuation properties for one dimensional higher order Schrödinger equations ⋮ \(H^p-H^q\) estimates for dispersive equations and related applications ⋮ Integrated groups and smooth distribution groups ⋮ Inhomogeneous oscillatory integrals and global smoothing effects for dispersive equations ⋮ 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 ⋮ Oscillatory integrals for phase functions having certain degenerate critical points ⋮ Dispersive Estimates with Geometry of Finite Type ⋮ Unique continuation properties of the higher order nonlinear Schrödinger equations in one dimension ⋮ Oscillatory integrals and \(L^p\) estimates for Schrödinger equations ⋮ Global estimates of fundamental solutions for higher-order Schrödinger equations ⋮ \(L^p-L^q\) estimates for dispersive equations and related applications

Cites Work

• Estimates for translation invariant operators in \(L^p\) spaces
• Damping oscillatory integrals
• Vector-valued Laplace transforms and Cauchy problems
• Convex hypersurfaces and Fourier transforms
• Smooth distribution group and Schrödinger equation in \(L^p(\mathbb{R}^n)\)
• Abstract parabolic systems and regularized semigroups
• Semigruppi regolarizzabili
• L p Estimates for Schrodinger Evolution Equations
• The Cauchy Problem and a Generalization of the Hille-Yosida Theorem
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