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

Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)411-422
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume471
Issue number1-2
DOIs
Publication statusPublished - Mar 2019

Keywords

  • Dispersive equations
  • Maximal-function estimates
  • Oscillatory integrals
  • Schrödinger equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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