Abstract
In this paper we consider functionsf(t), −∞ < t < ∞, which are n times continuously differentiable with a given convex modulus of continuity of the n-th derivative. For a certain class of periodic functions we establish a relationship between upper bounds of the absolute values of a function and its n-th derivative.
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A. N. Kolmogorov, “On inequalities between upper bounds of the derivatives of an arbitrary function studied on an infinite interval,” Uchen. Zap. Mosk. Gos. Un-ta,30, 3–16 (1939).
G. V. Kirsanova, “A relationship between the upper bounds of functions and their derivatives in certain classes,” Uchen. Zap. MOPI, Matem. Analiz,150, No. 9, 41–55 (1964).
G. V. Kirsanova, “A relationship between the absolute values of vector functions and their derivatives in a p-dimensional space,” Uchen. Zap. MOPI, Matem. Analiz,150, No. 9, 57–70 (1964).
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Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 329–338, September, 1973.
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Kirsanova, G.V. Relations between upper bounds of absolute values of functions and their higher derivatives. Mathematical Notes of the Academy of Sciences of the USSR 14, 749–754 (1973). https://doi.org/10.1007/BF01147449
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DOI: https://doi.org/10.1007/BF01147449