On certain trilinear oscillatory integral inequalities

Abstract Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms of Lebesgue space norms of the functions, and in terms of negative powers of large parameters describing a degree of oscillation. Related sublevel set inequalities are a central element of the analysis.