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December 2019 Sharp estimates for oscillatory integral operators via polynomial partitioning
Larry Guth, Jonathan Hickman, Marina Iliopoulou
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Acta Math. 223(2): 251-376 (December 2019). DOI: 10.4310/ACTA.2019.v223.n2.a2

Abstract

The sharp range of $L^p$-estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments. The main result implies improved bounds for the Bochner–Riesz conjecture in dimensions $n \geqslant 4$.

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Larry Guth. Jonathan Hickman. Marina Iliopoulou. "Sharp estimates for oscillatory integral operators via polynomial partitioning." Acta Math. 223 (2) 251 - 376, December 2019. https://doi.org/10.4310/ACTA.2019.v223.n2.a2

Information

Received: 6 November 2017; Published: December 2019
First available in Project Euclid: 16 April 2020

zbMATH: 1430.42016
MathSciNet: MR4047925
Digital Object Identifier: 10.4310/ACTA.2019.v223.n2.a2

Rights: Copyright © 2019 Institut Mittag-Leffler

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Vol.223 • No. 2 • December 2019
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