Sharp local smoothing for Fourier integral operators

D. Beltran, Jonathan Hickman, Christopher Sogge

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract / Description of output

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local smoothing estimates for a natural class of Fourier integral operators. We also show how local smoothing estimates imply oscillatory integral estimates and obtain a maximal variant of an oscillatory integral estimate of Stein. Together with an oscillatory integral counterexample of Bourgain, this shows that our local smoothing estimates are sharp in odd spatial dimensions. Motivated by related counterexamples, we formulate local smoothing conjectures which take into account natural geometric assumptions arising from the structure of the Fourier integrals.
Original languageEnglish
Title of host publicationProceedings of Geometric Aspects of Harmonic Analysis
EditorsPaolo Ciatti, Alessio Martini
PublisherSpringer, Cham
Pages29-105
ISBN (Electronic)978-3-030-72058-2
ISBN (Print)978-3-030-72057-5
DOIs
Publication statusPublished - 24 Feb 2021

Publication series

NameSpringer INdAM Series
Volume45
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

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