Abstract: Haberl and Ludwig introduced the L_p-intersection body I_pK for an origin-symmetric star body K in R_n, where p < 1 and p ≠ 0. In this paper, we consider the Busemann-Petty’s problem for L_p-intersection bodies I_pK and I_pL. That is, whether I_pK  I_pL implies Vol_n(K) ≤ Vol_n(L). We obtain that for two origin-symmetric star bodies K and L in Rn, such that (Rn, ||·||K) embeds in L_p and I_pK  IpL, then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0. 

Key words: star body, L_p-intersection bodies, isometrically embedded in L_p, generalized cosine transforms