We establish conditions for a system of positive numbers M k1, M k2, M k3, M k4, 0 = k 1 < k 2 < k 3 = r − 2, k 4 = r, necessary and sufficient for the existence of a function \( x\in {L^r}_{{\infty, \infty }}\left( \mathbb{R} \right) \) such that \( {{\left\| {{x^{{\left( {{k_i}} \right)}}}} \right\|}_{\infty }}={M_{{{k_i}}}},i=1,2,3,4 \).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 597–603, May, 2012.
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Babenko, V.F., Kovalenko, O.V. 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. Ukr Math J 64, 672–679 (2012). https://doi.org/10.1007/s11253-012-0670-9
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DOI: https://doi.org/10.1007/s11253-012-0670-9