Exact inequalities for derivatives of functions of low smoothness defined on an axis and a semiaxis - Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We obtain new exact inequalities of the form ∥x(k)∥_q ⩽ K∥x∥^α_p ∥x(r)∥^1−α_s for functions defined on the axis R or the semiaxis R_+ in the case where r = 2, k = 0, p ∈ (0,∞), q ∈ (0,∞], q > p, s=1, for functions defined on the axis R in the case where r = 2, k = 1, q ∈ [2,∞), p = ∞, s= 1, and for functions of constant sign on R or R_+ in the case where r = 2, k = 0, p ∈ (0,∞), q ∈ (0,∞], q > p, s = ∞ and in the case where r = 2, k = 1, p ∈ (0,∞), q = s = ∞.