This article is cited in 16 papers

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

A. S. Belov

Ivanovo State University

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.

UDC: 517.5

Received: 23.08.2001

DOI: 10.4213/mzm386

 English version: Mathematical Notes, 2002, 71:6, 739–748

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