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

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

doi:10.1016/j.jmaa.2018.10.082

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

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.1016/j.jmaa.2018.10.082
Publication status	Published - Mar 2019

Keywords

Dispersive equations
Maximal-function estimates
Oscillatory integrals
Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2018.10.082

Cite this

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title = "Transference of local to global L2 maximal estimates for dispersive partial differential equations",

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.",

keywords = "Dispersive equations, Maximal-function estimates, Oscillatory integrals, Schr{\"o}dinger equation",

author = "Castro, {Alejandro J.} and Salvador Rodr{\'i}guez-L{\'o}pez and Wolfgang Staubach",

note = "Funding Information: The first author is supported by Nazarbayev University Social Policy Grant and by the Spanish Government grant MTM2016-79436-P. The second author is partially supported by the Spanish Government grant MTM2016-75196-P. The third author is partially supported by a grant from the Crafoord Foundation (KVA 104650800) and by a grant from G. S. Magnusons fond, grant number MG2015-0077. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.jmaa.2018.10.082",

language = "English",

volume = "471",

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AU - Castro, Alejandro J.

AU - Rodríguez-López, Salvador

AU - Staubach, Wolfgang

N1 - Funding Information: The first author is supported by Nazarbayev University Social Policy Grant and by the Spanish Government grant MTM2016-79436-P. The second author is partially supported by the Spanish Government grant MTM2016-75196-P. The third author is partially supported by a grant from the Crafoord Foundation (KVA 104650800) and by a grant from G. S. Magnusons fond, grant number MG2015-0077. Publisher Copyright: © 2018 Elsevier Inc.

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N2 - 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.

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KW - Dispersive equations

KW - Maximal-function estimates

KW - Oscillatory integrals

KW - Schrödinger equation

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