On Trilinear Oscillatory Integral Inequalities and Related Topics

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 of negative powers of large parameters describing a degree of oscillation. Related sublevel set inequalities are a central element of the analysis. The main results and the main lines of their proofs are largely unchanged in this draft, but some details have been corrected. The analysis has already been extended in work of the author, Durcik, and Roos.

References in corpus (1)

• Bounds For Multilinear Sublevel Sets Via Szemeredi's Theorem

Cited by in corpus (5)

• Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
• On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem
• Pointwise convergence of certain continuous-time double ergodic averages
• Dimension-expanding polynomials and the discretized Elekes-Rónyai theorem
• The non-resonant bilinear Hilbert--Carleson operator