Sharp $L^p$ estimates for oscillatory integral operators of arbitrary signature

TL;DR

This paper establishes the precise range of L^p estimates for a broad class of oscillatory integral operators with arbitrary signature phases, generalizing previous results for specific signature cases.

Contribution

It provides the first sharp L^p bounds for oscillatory integral operators of any signature, extending earlier work limited to maximal or minimal signatures.

Findings

Established sharp L^p estimates for all signatures

Unified previous results for different signature cases

Extended the theory to more general phase functions

Abstract

The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase. This simultaneously generalises earlier work of the authors and Guth, which treats the maximal signature case, and also work of Stein and Bourgain--Guth, which treats the minimal signature case.