Oscillatory integrals and \(L^p\) estimates for Schrödinger equations

DOI10.1016/j.jde.2007.11.009zbMath1153.35016OpenAlexW2592440649MaRDI QIDQ2474058

Quan Zheng, Xiao Hua Yao

Publication date: 5 March 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.11.009

zbMATH Keywords

Schrödinger equationdegenerate conditionoscillatory integral\(L^p\) estimatefractionally integrated groupsintegrated group

Mathematics Subject Classification ID

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

Related Items

\(H^p-H^q\) estimates for dispersive equations and related applications ⋮ 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 ⋮ Dispersive Estimates with Geometry of Finite Type ⋮ 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
• Vector-valued Laplace transforms and Cauchy problems
• Convex hypersurfaces and Fourier transforms
• Existence families, functional calculi and evolution equations
• Abstract parabolic systems and regularized semigroups
• Convex hypersurfaces and \(L^p\) estimates for Schrödinger equations.
• L p Estimates for Schrodinger Evolution Equations
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