Restriction of Fourier transforms to curves: An endpoint estimate with affine arclength measure

Jong-Guk Bak, Daniel M. Oberlin, Andreas Seeger

Published 2011-09-06, updated 2012-03-17Version 2

Consider the Fourier restriction operator associated to a curve in $R^d$, $d\ge 3$. We prove for various classes of curves the endpoint restricted strong type estimate with respect to affine arclength measure on the curve. An essential ingredient is an interpolation result for multilinear operators with symmetries acting on sequences of vector-valued functions.