On the extension of differentiable functions from their monotonicity interval and inequalities of Kolmogorov type

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


We study the possibility of extension for every function $$$f\in L_{\infty}(\mathbb{R})$$$ from any monotonicity interval $$$I$$$ of function $$$f$$$ to the whole axis with retaining norms of $$$f$$$ and $$$f^{(r)}$$$ on interval.


Kolmogorov-type inequalities; the comparison theorem of Kolmogorov


Babenko V.F., Kofanov V.A., Pichugov S.A. "Exact constants of Kolmogorov type with bounded higher derivative in case of small smoothness", Ukrainian Math. J., 2001; 53(10): pp. 1298-1308. (in Russian) doi:10.1023/A:1015226223806

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)

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

DOI: https://doi.org/10.15421/241406



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