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

The sharp range of $$L^p$$ L p -estimates for the class of Hörmander-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.