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arXiv · 1612.09072

Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

Tianxiao Huang·Shanlin Huang·Quan Zheng
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Abstract

We study oscillatory integrals of the type ${\mathcal F}^{-1}(e^{ita(\cdot)}ψ(\cdot))$ where $a$ is a general function satisfying some elliptic type and non-degenerate conditions at both the origin and infinity, and $ψ$ 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.

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Tianxiao Huang, Shanlin Huang, Quan Zheng. 2017-01-30. Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations. https://doi.org/10.1016/j.jde.2017.08.053

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