Bilinear identities involving the k-plane transform and Fourier extension operators

Abstract

We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear identities: in particular, these are the analogues of a known identity for paraboloids, and may be seen as higher-dimensional versions of the classical L2pR2q-bilinear identity for Fourier extension operators associated to curves in R2.