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Mat. Zametki, 2006, Volume 80, Issue 5, Pages 701–711 (Mi mz3079)  

This article is cited in 5 scientific papers (total in 5 papers)

Refined theorems of approximation theory in the space of $p$-absolutely continuous functions

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky

Abstract: In this paper, we prove direct and inverse theorems of approximation theory in the space of $p$-absolutely continuous functions which generalize Terekhin's results in the same way as Timan's results in $L_p$ generalize the classical theorems of approximation theory. The main theorems are refined for functions with quasimonotone Fourier coefficients and, in a number of cases, the resulats are shown to be sharp.

DOI: https://doi.org/10.4213/mzm3079

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English version:
Mathematical Notes, 2006, 80:5, 663–672

Bibliographic databases:

UDC: 517.51
Received: 27.08.2003
Revised: 27.05.2006

Citation: S. S. Volosivets, “Refined theorems of approximation theory in the space of $p$-absolutely continuous functions”, Mat. Zametki, 80:5 (2006), 701–711; Math. Notes, 80:5 (2006), 663–672

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chikina T.S., “Approximation by Zygmund-Riesz Means in the P-Variation Metric”, Anal. Math., 39:1 (2013), 29–44  crossref  mathscinet  isi  elib  scopus
    2. A. A. Tyuleneva, “Asymptotic estimates of $p$-variational and $L^p$-moduli of continuity of functions of certain classes”, Russian Math. (Iz. VUZ), 60:11 (2016), 58–68  mathnet  crossref  isi
    3. Volosivets S.S. Tyuleneva A.A., Acta Sci. Math., 82:1-2 (2016), 111–124  crossref  mathscinet  zmath  isi  elib  scopus
    4. Volosivets S.S. Tyuleneva A.A., “Approximation of Functions and Their Conjugates in l-P and Uniform Metric By Euler Means”, Demonstr. Math., 51:1 (2018), 141–150  crossref  mathscinet  zmath  isi
    5. S. S. Volosivets, A. A. Tyuleneva, “Otsenki nailuchshikh priblizhenii preobrazovannykh ryadov Fure v $L^p$-norme i $p$-variatsionnoi norme”, Fundament. i prikl. matem., 22:1 (2018), 111–126  mathnet
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