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

Jonathan Hickman, Marina Iliopoulou

Published 2020-06-01Version 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 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.