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.
| Original language | English |
|---|---|
| Pages (from-to) | 411-422 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 471 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - Mar 2019 |
Keywords
- Dispersive equations
- Maximal-function estimates
- Oscillatory integrals
- Schrödinger equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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Castro, A. J., Rodríguez-López, S., & Staubach, W. (2019). Transference of local to global L2 maximal estimates for dispersive partial differential equations. Journal of Mathematical Analysis and Applications, 471(1-2), 411-422. https://doi.org/10.1016/j.jmaa.2018.10.082