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Oscillatory integral operators with homogeneous phase functions

Schippa, Robert 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)

Abstract:

Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the Lp–Lp-estimates for the Fourier extension operator of the cone due to Ou–Wang via polynomial partitioning. For this purpose, we combine the arguments of Ou–Wang with the analysis of Guth–Hickman–Iliopoulou, who previously showed sharp Lp–Lp-estimates for non-homogeneous phase functions with variable coefficients under a convexity assumption. Furthermore, we provide examples exhibiting Kakeya compression, which shows a more restrictive range than dictated by the Knapp example in higher dimensions. We apply the oscillatory integral estimates to show new local smoothing estimates for wave equations on compact Riemannian manifolds (M, g) with dim M ≥ 3. This generalizes the argument for the Euclidean wave equation due to Gao–Liu–Miao–Xi.


Verlagsausgabe §
DOI: 10.5445/IR/1000166947
Veröffentlicht am 04.01.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2023
Sprache Englisch
Identifikator ISSN: 0021-7670, 1565-8538
KITopen-ID: 1000166947
Erschienen in Journal d'Analyse Mathématique
Verlag Hebrew University Magnes Press
Vorab online veröffentlicht am 12.12.2023
Nachgewiesen in Scopus
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