Sharp estimates for oscillatory integral operators via polynomial partitioning
Classical Analysis and ODEs
2019-09-26 v2
Abstract
The sharp range of -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.
Cite
@article{arxiv.1710.10349,
title = {Sharp estimates for oscillatory integral operators via polynomial partitioning},
author = {Larry Guth and Jonathan Hickman and Marina Iliopoulou},
journal= {arXiv preprint arXiv:1710.10349},
year = {2019}
}
Comments
Updated version incorporating minor corrections, additional clarification and an expanded discussion of applications. 95 pages. 6 figures. To appear Acta. Math