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In this note we will prove a (L , LP) -restriction theorem for certain submanifolds & of codimension / > 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 1 < p < j^y. We will show that for the submanifolds under consideration the inequality ^\f(x)\ 2 dKx)<C'\\f\\ 2 p holds for 1 < p < ^3f . Thus we give an answer to a problem stated by J. L. Clerc in [CL, p. 58].doi:10.1090/s0273-0979-1991-16018-0 fatcat:4g2inmwl3bgori4j4qkqqtd5a4