Decoupling for mixed-homogeneous polynomials in $\mathbb R^3$

TL;DR

This paper establishes decoupling inequalities for mixed-homogeneous bivariate polynomials in three-dimensional space, advancing understanding in harmonic analysis and partially resolving a conjecture by Bourgain, Demeter, and Kemp.

Contribution

It introduces new decoupling inequalities specifically for mixed-homogeneous polynomials, addressing a significant open conjecture in the field.

Findings

Proved decoupling inequalities for mixed-homogeneous bivariate polynomials

Partially answered a conjecture of Bourgain, Demeter, and Kemp

Enhanced understanding of harmonic analysis techniques

Abstract

We prove decoupling inequalities for mixed-homogeneous bivariate polynomials, which partially answers a conjecture of Bourgain, Demeter and Kemp.