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L2-estimates for singular oscillatory integral operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
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, p. 529-548Article in journal (Refereed) Published
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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, p. 529-548
Keywords [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: 000375635300002Scopus ID: 2-s2.0-84963859665OAI: oai:DiVA.org:kth-187381DiVA, id: diva2:931361
Note

QC 20160527

Available from: 2016-05-27 Created: 2016-05-23 Last updated: 2017-06-20Bibliographically approved

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Shahgholian, Henrik

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