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

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Matematicheskie Zametki, 2006, Volume 80, Issue 5, Pages 701–711
DOI: https://doi.org/10.4213/mzm3079 (Mi mzm3079)

This article is cited in 7 scientific papers (total in 7 papers)

Refined theorems of approximation theory in the space of

p

$p$ -absolutely continuous functions

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky

Full-text PDF (486 kB) Citations (7)

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

Abstract: In this paper, we prove direct and inverse theorems of approximation theory in the space of

p

$p$ -absolutely continuous functions which generalize Terekhin's results in the same way as Timan's results in

L_{p}

$L_p$ 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.

Received: 27.08.2003
Revised: 27.05.2006

English version:
Mathematical Notes, 2006, Volume 80, Issue 5, Pages 663–672
DOI: https://doi.org/10.1007/s11006-006-0187-3

Bibliographic databases:

UDC: 517.51

Language: Russian

Citation: S. S. Volosivets, “Refined theorems of approximation theory in the space of

p

$p$ -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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Linking options:

https://www.mathnet.ru/eng/mzm3079

https://doi.org/10.4213/mzm3079

https://www.mathnet.ru/eng/mzm/v80/i5/p701

This publication is cited in the following 7 articles:

S. S. Volosivets, S. A. Krayukhin, “Criteria for a Function to Belong to the $p$ -Variational Besov Space”, Math. Notes, 109:1 (2021), 21–28
Golubov B. Volosivets S., “On Some Sharp Conditions For Generalized Absolute Convergence of Fourier Series”, Trans. A Razmadze Math. Inst., 175:3 (2021), 347–355
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
S. S. Volosivets, A. A. Tyuleneva, “Estimates of best approximations of transformed Fourier series in $L^p$ -norm and $p$ -variational norm”, J. Math. Sci., 250:3 (2020), 463–474
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
Volosivets S.S. Tyuleneva A.A., Acta Sci. Math., 82:1-2 (2016), 111–124
Chikina T.S., “Approximation by Zygmund-Riesz Means in the P-Variation Metric”, Anal. Math., 39:1 (2013), 29–44

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	68
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