On the dependence of the norm of a function on the norms of its derivatives of orders k , r - 2 and r , 0 < k < r - 2 - Babenko, V. F.; Kovalenko, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We establish conditions for a system of positive numbers M_k_1, M_k_2, M_k_3, M_k_4, 0 = k_1 < k2 < k3 = r − 2, k4 = r, necessary and sufficient for the existence of a function x L^r_∞, ∞(R) such that ||x^(k_i) ||_∞ = M_k_i,i = 1, 2, 3, 4.