Abstract: In we introduced spaces L_ρ (φ), E_ρ(φ). In this paper we shall take the L_ρ(φ)-norm in stead of L_ρ-norm in the Spaces B_p,q(r), then we get the spaces B_p,q(r)(φ). we prove a trace theorem of the spaces B_p,q(r)(φ) and we can apply this method to the estimate of difference method of the initial problem.