Transference of local to global $L^2$ maximal estimates for dispersive partial differential equations
Analysis of PDEs
2023-10-25 v1
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 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.
Keywords
Cite
@article{arxiv.1712.02539,
title = {Transference of local to global $L^2$ maximal estimates for dispersive partial differential equations},
author = {Alejandro J. Castro and Salvador Rodríguez-López and Wolfgang Staubach},
journal= {arXiv preprint arXiv:1712.02539},
year = {2023}
}
Comments
10 pages