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- W2040732374 abstract "Let ${ c(n)}$ be a complex null sequence such that for some integer $m geq 1$ and some $p in (1,2]$ [ sum limits _{|n| < infty } {|{Delta ^m}c(n){|^p} < infty quad {text {and}}quad sum limits _{n = 1}^infty {|Delta (c(n) - c( - n))|lg n < infty .} } ] It is shown that the series [ ( * )quad sum limits _{|n| < infty } {c(n)} {e^{operatorname {int} }},quad t in T = frac {mathbb {R}}{{2pi mathbb {Z}}}] converges a.e. and that the well-known condition ${C_w}$ of J. W. Garrett and C. V. Stanojevic [4, 3] implies that the series (*) is the Fourier series of its sum. This generalizes results of W. O. Bray and C. V. Stanojevic [1]. An important consequence of the main result is that $nDelta c(n) = 0(1),quad |n| to infty$, implies that the condition ${C_w}$ is equivalent to the de la Vallee Poussin summability of partial sums ${ {S_n}(c)}$ as conjectured in [8]." @default.
- W2040732374 created "2016-06-24" @default.
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- W2040732374 date "1992-03-01" @default.
- W2040732374 modified "2023-09-25" @default.
- W2040732374 title "Convergence and integrability of trigonometric series with coefficients of bounded variation of order $(m,p)$" @default.
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- W2040732374 doi "https://doi.org/10.1090/s0002-9939-1992-1068132-0" @default.
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