Year: 2022
Type: preprint
Abstract: For functions $f$ with Fourier transform supported in the truncated cone, we bound superlevel sets $\{x\in\mathbb{R}^3:|f(x)|>α\}$ using an $α$-dependent version of the wave envelope estimate of Guth--Wang--Zhang. Our estimates imply both sharp square function and decoupling inequalities for the cone. We also obtain sharp small cap decoupling for the cone, where small caps $γ$ subdivide canonical $1\times R^{-1/2}\times R^{-1}$ planks into $R^{-β_2}\times R^{-β_1}\times R^{-1}$ sub-planks, for $β_1\in[\frac{1}{2},1]$ and $β_2\in[0,1]$.
Source: arXiv (Cornell University)
Authors: Maldague, Dominique, Guth, Larry
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4281638174