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Matematicheskie Zametki, 2002, Volume 71, Issue 6, Pages 807–817
DOI: https://doi.org/10.4213/mzm386 (Mi mzm386) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series

A. S. Belov

Ivanovo State University
Full-text PDF (214 kB) Citations (16)
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DOI: https://doi.org/10.4213/mzm386
Abstract: Fairly general conditions on the coefficients $\{a_n\}_{n=1}^\infty$ of even and odd trigonometric Fourier series under which $L$-convergence (boundedness) of partial sums of the series is equivalent to the relation $\sum _{k=[n/2]}^{2n}|a_k|/(|n-k|+1)=o(1)$ ($=O(1)$, respectively) are given.
Received: 23.08.2001
English version:
Mathematical Notes, 2002, Volume 71, Issue 6, Pages 739–748
DOI: https://doi.org/10.1023/A:1015860510199
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: A. S. Belov, “Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series”, Mat. Zametki, 71:6 (2002), 807–817; Math. Notes, 71:6 (2002), 739–748
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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