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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 $p$-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 $p$-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.
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 $p$-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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  • 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:
    1. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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  mathscinet  isi
    3. 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
    4. 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  mathnet  crossref
    5. 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
    6. Volosivets S.S. Tyuleneva A.A., Acta Sci. Math., 82:1-2 (2016), 111–124  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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