Abstract: Let 0<k<n,and k-dinensional object SCR°.Also,S will come with a nonnegative Radon measure u on R"such that suppu=S.Define the Fourier restriction operator T by ... ,holds for all f∈C(R")and some redial weighted funcion vifS is a bounded surface and u∈4.Here 1 ≤p<0.Our reslut generalizes those in  [6] to  some  extent.

Key words: restriction theorem, fourier transfrom