Uniform estimates for Fourier restriction to polynomial curves in Rd\mathbb R^d

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.Comment: This is a preprint version of a published article. The final version is in Amer. J. Math. 138 (2016), no. 2, 449--47

Endpoint bounds for a generalized {R}adon transform

We prove that convolution with affine arclength measure on the curve parametrized by $h(t) := (t,t^2,...,t^n)$ is a bounded operator from $L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.Comment: 24 pages, The final version of this article will appear in the Journal of the London Math. So