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

Alejandro J. Castro Castilla, 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.

LanguageEnglish
Pages411-422
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume471
Issue number1-2
DOIs
Publication statusPublished - Mar 1 2019

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Wave packets
Partial differential equations
Partial differential equation
Oscillatory Integrals
Estimate
Wave Packet
Rough
Scaling

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Transference of local to global L2 maximal estimates for dispersive partial differential equations. / Castro Castilla, Alejandro J.; Rodríguez-López, Salvador; Staubach, Wolfgang.

In: Journal of Mathematical Analysis and Applications, Vol. 471, No. 1-2, 01.03.2019, p. 411-422.

Research output: Contribution to journalArticle

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