On Trilinear Oscillatory Integrals

TL;DR

This paper investigates a class of trilinear oscillatory integrals involving polynomial phases and demonstrates that these integrals diminish in magnitude when the oscillations are rapid, highlighting their decay properties.

Contribution

The paper provides new decay estimates for trilinear oscillatory integrals with polynomial phases, advancing understanding of their behavior under rapid oscillations.

Findings

Proves decay of trilinear oscillatory integrals with polynomial phases.

Establishes bounds showing smallness of integrals with rapid oscillations.

Enhances theoretical understanding of oscillatory integral operators.

Abstract

We examine a certain class of trilinear integral operators which incorporate oscillatory factors e^{iP}, where P is a real-valued polynomial, and prove smallness of such integrals in the presence of rapid oscillations.