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

References


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

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

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

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. (in Russian)

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. (in Russian) 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 Mathematique, 1999; 78: pp. 263-280. doi:10.1007/BF02791137

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)

Akhiezer N.I. Lectures on Approximation Theory, Moscow, Nauka, 1965; 407 p. (in Russian)

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

Taikov L.V. "On one generalization of Bernstein inequality", Trudy matem. in-ta im. V.A. Steklova, 1965; 78: pp. 43-47. (in Russian)




DOI: https://doi.org/10.15421/241014

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 V.A. Kofanov

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU