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Literature cited
V. N. Gabushin, “Inequalities for norms of functions and its derivatives in Lp metrics,” Mat. Zametki, No. 3, 291–298 (1967).
A. N. Kolmogorov, “Inequalities between upper bounds of successive derivatives of an arbitrary function on an infinite interval,” Uch. Zap. Mosk. Univ., Ser. Mat.,30, 3–16 (1939).
V. A. Markov, On Functions with the Least Deviation from Zero at a Given Interval [in Russian], St. Petersburg (1892).
V. V. Arestov, “Some extremal problems for differentiable functions of one variable,” Trudy Mat. Inst. Akad. Nauk SSSR,138, 3–28 (1975).
V. I. Burenkov, “Exact constants in inequalities for norms of the intermediate derivatives on a finite interval,” Trudy Mat. Inst. Akad. Nauk SSSR,156, 22–29 (1980).
M. V. Novitskii, “Bilateral estimates of polynomial conservation laws for the KdV equation and their applications,” Funkts. Anal. Ego Prilozh.,23, No. 3, 78–79 (1989).
V. N. Gabushin, “Inequalities satisfied by derivatives of solutions of ordinary differential equations in metrics Lp (0<p<∞),” Differents, Uravn.,24, No. 10, 1662–1670 (1988).
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Translated from Matematicheskie Zametki, Vol. 53, No. 3, pp. 80–91, March, 1993.
The author thanks V. I. Burenkov for drawing his attention to the paper [5] and for subsequent discussions of the results obtained.
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Novitskii, M.V. An analog of an inequality of the Kolmogorov-Markov type for ordinary differential operations. Math Notes 53, 300–308 (1993). https://doi.org/10.1007/BF01207717
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DOI: https://doi.org/10.1007/BF01207717