Literature cited
A. N. Kolmogorov, “On the inequalities between the suprema of the successive derivatives of an arbitrary function on an infinite interval,” Uch. Zap. Mosk. Gos. Univ.,30, 3–16 (1939).
V. N. Gabushin, “Inequalities for the norms of a function and its derivatives in the metrics of Lp,” Mat. Zametki,1, No. 3, 291–298 (1967).
V. M. Tikhomirov, Certain Problems of Approximation Theory [in Russian], Moscow State Univ. (1976).
G. H. Hardy, D. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge (1964).
Yu. N. Subbotin and L. V. Taikov, “The best approximation of the operator of differentiation in the space L2,” Mat. Zametki,3, No. 2, 157–164 (1968).
E. M. Stein, “Functions of exponential type,” Ann. Math.,65, No. 3, 582–592 (1957).
L. V. Taikov, “Kolmogorov-type inequalities and best formulas for numerical differentiation,” Mat. Zametki,4, No. 2, 233–238 (1968).
B. Sz. Nagy, “Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung,” Acta Sci. Math.,10, 64–74 (1941).
V. V. Arestov, “On sharp inequalities between the norms of functions and their derivatives,” Acta Sci. Math. Szeged,33, Nos. 3–4, 243–267 (1972).
V. N. Gabushin, “Sharp constants in the inequalities between the norms of the derivatives of functions,” Mat. Zametki,4, No. 2, 221–232 (1968).
S. B. Stechkin, “Inequalities between the norms of the derivatives of an arbitrary function,” Acta Sci. Math. Szeged,26, Nos. 3–4, 225–230 (1965).
N. P. Kuptsov, “The Kolmogqrov estimates for derivatives in L2 (0, ∞),” Tr. Mat. Inst. Akad. Nauk SSSR,138, 94–118 (1975).
V. I. Berdyshev, “The best approximation in L(0, ∞) of the operator of differentiation,” Mat. Zametki,9, No. 5, 477–481 (1971).
V. N. Gabushin, “On the best approximation of the operator of differentiation on the halfline,” Mat. Zametki,6, No. 5, 573–582 (1969).
V. I. Burenkov, “On exact constants in the inequalities for the norms of intermediate derivatives on a finite interval,” Tr. Mat. Inst. Akad. Nauk SSSR,156, 22–29 (1980).
S. Z. Rafal'son, “On the approximation of functions by the Fourier-Jacobi sums,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 54–62 (1968).
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Translated from Matematicheskie Zametki, Vol. 33, No. 1, pp. 77–82, January, 1983.
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Rafal'son, S.Z. An inequality between the norms of a function and its derivatives in integral metrics. Mathematical Notes of the Academy of Sciences of the USSR 33, 38–41 (1983). https://doi.org/10.1007/BF01141198
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DOI: https://doi.org/10.1007/BF01141198