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L2-estimates for singular oscillatory integral operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 441, no 2, 529-548 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2L2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R3.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 441, no 2, 529-548 p.
Keyword [en]
Helmholtz equation, Maximal operator, Oscillating surface, Singular integral
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-187381DOI: 10.1016/j.jmaa.2016.04.031ISI: 000375635300002ScopusID: 2-s2.0-84963859665OAI: oai:DiVA.org:kth-187381DiVA: diva2:931361
Note

QC 20160527

Available from: 2016-05-27 Created: 2016-05-23 Last updated: 2016-06-09Bibliographically approved

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Shahgholian, HenrikSjölin, Per
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