Estimate of derivatives of functions on the real line in Weil spaces

V.A. Kofanov

doi:10.15421/240911

Estimate of derivatives of functions on the real line in Weil spaces

V.A. Kofanov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0003-0392-2257

Abstract

We prove the inequality that estimates seminorm of Weil of the derivatives of the functions on the real line with the help of uniform norm of the functions and their derivatives. We also solve the corresponding problem of Kolmogorov.

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References

Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, Kyiv, 2003; 590 p. (in Russian)

Babenko V.F. "Researches of Dnipropetrovsk mathematicians on inequalities for derivatives of periodic functions and their applications", Ukrainian Math. J., 2000, 52(1): pp. 9-29. (in Russian) doi:10.1007/BF02514133

Kwong M.K., Zettl A. "Norm inequalities for derivatives and differences", Lecture notes in mathematics, 1993; 1536: 150 p.

Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", J. d'Analyse Mathematique, 1999; 78: pp. 263-280. doi:10.1007/BF02791137

Levitan B.M. Almost periodic functions, Moscow, 1953; 396 p. (in Russian)

Ligun A.A. "Inequalities for upper bounds of functionals", Analysis Math., 1976; 2(1): pp. 11-40. doi:10.1007/BF02079905

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on the infinite interval", Izbr. tr.: Matematika, mechanika, Moscow, 1985; pp. 252-263. (in Russian)