Uniform $l^2$-decoupling in ${\mathbb{R}}^2$ for Polynomials

Abstract

For each positive integer $d$, we prove a uniform $l^2$-decoupling inequality for the collection of all polynomials phases of degree at most $d$. Our result is intimately related to \cite{MR4078083}, but we use a different partition that is determined by the geometry of each individual phase function.

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