On some inequalities in various metrics for differentiable functions on real line

V.A. Kofanov

doi:10.15421/241014

On some inequalities in various metrics for differentiable functions on real line

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

Abstract

We obtain the estimates of the seminorms of Weil of the functions on the real line and their derivatives with the help of local $$$L_p$$$-norms of the functions and uniform norms of their highest derivatives.

Keywords

inequalities for derivatives; seminorms of Weil

Full Text:

PDF (Русский)

References

Pinkus A., Shisha O. "Variations on the Chebyshev and $$$L^q$$$-Theories of Best Approximation", J. Approx. Theory, 1982; 35(2): pp. 148-168. doi:10.1016/0021-9045(82)90033-8

Kofanov V.A. "Some extremum problems in different metrics for differentiable functions in the real domain", Ukrainian Math. J., 2009; 61(6): pp. 765-776. doi:10.1007/s11253-009-0254-5

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

Calderon A.P., Klein G. "On an extremum problem concerning trigonometrical polynomials", Studia Math., 1951; 12: pp. 166-169. doi:10.4064/sm-12-1-166-169

Levitan B.M. Almost periodic functions, 1953; 396 p.

Kofanov V.A. "Estimate of derivatives of functions on real line in Weil spaces", Res. Math., 2009; 17: pp. 80-84.

Kofanov V.A. "On sharp inequalities of Kolmogorov and Bernstein type", Pratsі Ukrajins'kogo matematychnogo kongresu (Approximation theory and Fourier analysis), 2001, Kyiv, 2002; pp. 84-99.

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on the infinite interval", Izbr. trudy: Matem., mech., 1985; pp. 252-263.

Akhiezer N.I. Lectures on Approximation Theory, Nauka, 1965.

Taikov L.V. "On one generalization of Bernstein inequality", Trudy matem. inst. Steklova, 1965; 78: pp. 43-47.