Sharp estimates for oscillatory integral operators via polynomial partitioning

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.

Updated version incorporating minor corrections, additional clarification and an expanded discussion of applications. 95 pages. 6 figures. To appear Acta. Math