Sharp estimates for oscillatory integral operators via polynomial partitioning

Larry Guth, Jonathan Hickman, Marina Iliopoulou

Published 2017-10-27Version 1

The sharp range of $L^p$-estimates for the class of H\"ormander-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.