# Special cases of power decay in multilinear oscillatory integrals

## TL;DR

This paper extends the understanding of power decay in multilinear oscillatory integrals by analyzing special cases not covered by existing theories, thereby broadening the class of integrals with known decay properties.

## Contribution

It introduces new techniques to handle special cases of multilinear oscillatory integrals, expanding the theoretical framework for power decay.

## Key findings

- Extended class of integrals with $mbda$-power decay
- New methods for analyzing special cases
- Broader applicability of decay results

## Abstract

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Consideration of special cases leads to an extended class of examples for which $\lambda$-power decay holds.