Optimal weighted Fourier restriction estimates for the sphere in 2D

Abstract

We prove weighted versions of the 2D Restriction Conjecture for the unit sphere in ${\mathbb{R}}^2$. Our results involve the weight functions $(1+|x|{)}^{\alpha }(1+|y|{)}^{\beta }$ and $(1+|x|+|y|{)}^{\gamma }$ with $\alpha ,\beta ,\gamma \ge 0$.