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 $n \geqslant 4$.
Citation
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