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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 1, Pages 171–192
DOI: https://doi.org/10.1070/IM1977v011n01ABEH001698
(Mi im1796)
 

This article is cited in 3 scientific papers (total in 3 papers)

Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions

E. P. Dolzhenko, V. I. Danchenko
References:
Abstract: Let $E$ be a Lebesgue measurable subset of a $k$-dimensional cube ($k\geqslant1$), let $f\in L_p[E]$, where $0<p\leqslant\infty$, and let $R_n[f,p,E]$ be the least deviation of $f$, in the metric of $L_p[E]$, from the rational functions of degre $\leqslant n$. If $R_n[f,p,E]=O(n^{-\lambda})$, then, for $0<\mu<\lambda$, $f$ has a local differential of order $\mu$ in the $L_p$-metric at each point $\xi\in E$, except perhaps points $\xi$ of some set of metric dimension $\leqslant k-1+(p\mu+1)/(p\lambda+1)$ (this inequality is sharp). In addition, $f$ has a global differential of order $\mu$ in the metric of $L_q [E]$ for any $q<p/(p\mu+1)$.
Bibliography: 15 titles.
Received: 20.04.1976
Bibliographic databases:
UDC: 517.5
MSC: 41A20
Language: English
Original paper language: Russian
Citation: E. P. Dolzhenko, V. I. Danchenko, “Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions”, Math. USSR-Izv., 11:1 (1977), 171–192
Citation in format AMSBIB
\Bibitem{DolDan77}
\by E.~P.~Dolzhenko, V.~I.~Danchenko
\paper Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 171--192
\mathnet{http://mi.mathnet.ru//eng/im1796}
\crossref{https://doi.org/10.1070/IM1977v011n01ABEH001698}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=442550}
\zmath{https://zbmath.org/?q=an:0355.41020|0392.41007}
Linking options:
  • https://www.mathnet.ru/eng/im1796
  • https://doi.org/10.1070/IM1977v011n01ABEH001698
  • https://www.mathnet.ru/eng/im/v41/i1/p182
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:1406
    Russian version PDF:155
    English version PDF:13
    References:48
    First page:1
     
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