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Transference of local to global L-2 maximal estimates for dispersive partial differential equations
Nazarbayev Univ, Dept Math, Astana 010000, Kazakhstan.
Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 471, no 1-2, p. 411-422Article in journal (Refereed) Published
Abstract [en]

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 L-2 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.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 471, no 1-2, p. 411-422
Keywords [en]
Oscillatory integrals, Maximal-function estimates, Dispersive equations, Schrodinger equation
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-372866DOI: 10.1016/j.jmaa.2018.10.082ISI: 000452581100022OAI: oai:DiVA.org:uu-372866DiVA, id: diva2:1277318
Available from: 2019-01-10 Created: 2019-01-10 Last updated: 2019-01-10Bibliographically approved

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Staubach, Wolfgang

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