In the case 1 ≤ p < q ≤ ∞, the question on the exact constant in the embedding of the space W_p¹ (0.1) into the space L_q(0.1) is studied, i.e., min ∥y∥W_p^l/∥y∥L_q = λ_pq > 0, where the norm is defined by the equality ∥y∥_Wpl^p = ∥y′∥_Lp^p + ∥y∥_Lp^p. Bibliography: 5 titles.