Uniform estimates for the local restriction of the Fourier transform to curves

Abstract

We prove sharp estimates, with respect to the affine arclength measure, for the restriction of the Fourier transform to a class of curves in $\mathbb {R}^d$ that includes curves of finite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results.

Locations

• Transactions of the American Mathematical Society - View - PDF