Acta Mathematica

Sharp estimates for oscillatory integral operators via polynomial partitioning

Larry Guth, Jonathan Hickman, and Marina Iliopoulou

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

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

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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.

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