# Decoupling for certain quadratic surfaces of low co-dimensions

## TL;DR

This paper establishes precise decoupling inequalities for two quadratic forms in four variables, unifying and extending previous results in harmonic analysis related to quadratic surfaces.

## Contribution

It provides sharp $ ext{ell}^p ext{L}^p$ decoupling inequalities for specific quadratic surfaces, unifying multiple earlier findings.

## Key findings

- Proved sharp decoupling inequalities for quadratic forms in four variables.
- Unified previous results into a single framework.
- Extended the scope of decoupling inequalities for quadratic surfaces.

## Abstract

We prove sharp $\ell^{p}L^{p}$ decoupling inequalities for $2$ quadratic forms in $4$ variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:1609.02022, arXiv:1609.04107) in a unified way.