English

Sharp estimates for oscillatory integral operators via polynomial partitioning

Classical Analysis and ODEs 2019-09-26 v2

Abstract

The sharp range of LpL^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.

Keywords

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

R2 v1 2026-06-22T22:28:11.799Z