Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

Abstract

We study oscillatory integrals of the type ${\mathcal{F}}^{-1}(e^{ita(\cdot )}\psi (\cdot ))$ where $a$ is a general function satisfying some elliptic type and non-degenerate conditions at both the origin and infinity, and $\psi$ belongs to some symbol class. Point-wise estimates in space-time are gained with partial sharpness. As applications, global smoothing effects of $L^p-L^q$ as well as Strichartz type for dispersive equations are studied. An application to fractional Schrödinger equations is also given.

22 pages, 1 figure

References in corpus (2)

• Decay estimates for a class of wave equations
• Sharp $L^p$ estimates for Schrödinger groups

Cited by in corpus (4)

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• Unique continuation properties for one dimensional higher order Schrödinger equations
• On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle
• Uniform Complex Time Heat Kernel Estimates Without Gaussian Bounds