Konstantinos Bampouras

Boundary-Weighted Fourier Inequalities for Convex Domains

We consider the natural family of Fourier inequalities for the Paley--Wiener space $\mathrm{PW}^q(\Omega)$, consisting of $L^q$-functions with Fourier support in a convex set $\Omega \subset \mathbb{R}^n$, $n \geq 2$, free of affine lines. Namely, \[ \int_{\Omega}\dfrac{|\hat{f}(x)|^p}{\omega_{\Omega}^d(x)}dx\leq C\|f\...