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 journal › Article

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
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Publication statusSubmitted - Aug 3 2018

Fingerprint

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

Cite this

Castro Castilla, A. J., Rodríguez-López, S., & Staubach, W. (2018). Transference of local to global L2 maximal estimates for dispersive partial differential equations. Manuscript submitted for publication.

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, 03.08.2018.

Research output: Contribution to journal › Article

Castro Castilla, AJ, Rodríguez-López, S & Staubach, W 2018, 'Transference of local to global L2 maximal estimates for dispersive partial differential equations', Journal of Mathematical Analysis and Applications.
Castro Castilla AJ, Rodríguez-López S, Staubach W. Transference of local to global L2 maximal estimates for dispersive partial differential equations. Journal of Mathematical Analysis and Applications. 2018 Aug 3.
Castro Castilla, Alejandro J. ; Rodríguez-López, Salvador ; Staubach, Wolfgang. / Transference of local to global L2 maximal estimates for dispersive partial differential equations. In: Journal of Mathematical Analysis and Applications. 2018.
@article{1ab307f8e87d4bee843a5be7603885dd,
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.",
author = "{Castro Castilla}, {Alejandro J.} and Salvador Rodr{\'i}guez-L{\'o}pez and Wolfgang Staubach",
year = "2018",
month = "8",
day = "3",
language = "English",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Transference of local to global L2 maximal estimates for dispersive partial differential equations

AU - Castro Castilla, Alejandro J.

AU - Rodríguez-López, Salvador

AU - Staubach, Wolfgang

PY - 2018/8/3

Y1 - 2018/8/3

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.

AB - 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.

M3 - Article

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -