论文标题
$ \ mathbb {r}^3 $中圆锥的振幅依赖性波信封估计值
Amplitude dependent wave envelope estimates for the cone in $\mathbb{R}^3$
论文作者
论文摘要
对于功能$ f $，在截短的锥体中支持傅立叶变换，我们使用$ a $依赖性的Wave Inveloper版本的Wave Invelope估算Guth-imate Matemate of Guth-– wang-wang-wang-zhang的$ \ f（x）^3：| f（x）|> <（x）|>α\} $。我们的估计既意味着圆锥形的尖锐的正方形功能和脱钩不平等。我们还获得了圆锥的锋利的小帽子脱钩，其中小帽子$γ$ subdivide $ 1 \ times r^{ - 1/2} \ times r^{ - 1} $ planks成$ r^{ - β_2} - β_2} \ times r^{ - β_1} $β_1\在[\ frac {1} {2}，1] $和$β_2\ in [0,1] $中。
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 $β_2\in[0,1]$.
