Acta Mathematica

Sharp estimates for oscillatory integral operators via polynomial partitioning

Larry Guth, Jonathan Hickman, and Marina Iliopoulou

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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 $n \geqslant 4$.

Article information

Source
Acta Math., Volume 223, Number 2 (2019), 251-376.

Dates
Received: 6 November 2017
First available in Project Euclid: 16 April 2020

Permanent link to this document
https://projecteuclid.org/euclid.acta/1587002465

Digital Object Identifier
doi:10.4310/ACTA.2019.v223.n2.a2

Mathematical Reviews number (MathSciNet)
MR4047925

Zentralblatt MATH identifier
1430.42016

Citation

Guth, Larry; Hickman, Jonathan; Iliopoulou, Marina. Sharp estimates for oscillatory integral operators via polynomial partitioning. Acta Math. 223 (2019), no. 2, 251--376. doi:10.4310/ACTA.2019.v223.n2.a2. https://projecteuclid.org/euclid.acta/1587002465


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