Title

Convergence and integrability of trigonometric series with coefficients of bounded variation of order (m, p)

Abstract

Converges a.e. and that the well-known condition Cw 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 nΔc(n) = 0(1), ƖnƖ → ∞, implies that the condition Cw is equivalent to the de la Valláe Poussin summability of partial sums (Sn(c)) as conjectured in [8]. © 1992 American Mathematical Society.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9939-1992-1068132-0

Keywords

Convergence and integrability of trigonometric series, Sequences of bounded variation of order (m, p)

Publication Date

1-1-1992

Journal Title

Proceedings of the American Mathematical Society

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