A restriction theorem for the fourier transform

Abstract

In this note we will prove a (L2, Lp) -restriction theorem for certain submanifolds (Equation presented) of codimension 1 > 1 in an n-dimensional Euclidean space which arise as orbits under the action of a compact group K. As is well known such a result can in general only hold for (Equation presented). We will show that for the submanifolds under consideration the inequality (Equation presented) holds for (Equation presented). Thus we give an answer to a problem stated by J. L. Clerc in [CL, p. 58]. © 1991 American Mathematical Society.