Transference of local to global L2 maximal estimates for dispersive partial differential equations

2019

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DOI 10.1016/j.jmaa.2018.10.082
Data confidence 70 medium
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Abstract

In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local L2 estimates for certain oscillatory integrals with rough phase functions, to the corresponding global estimates. The elementary feature of our approach is that it entirely avoids the use of the wave packet techniques which are quite common in this context, and instead is based on scalings and classical oscillatory integral estimates.