On certain sums of Fourier-Stieltjes coefficients

Twomey, J. B.

doi:10.1090/S0002-9947-1983-0716840-X

On certain sums of Fourier-Stieltjes coefficients
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by J. B. Twomey

Trans. Amer. Math. Soc. 280 (1983), 611-621

DOI: https://doi.org/10.1090/S0002-9947-1983-0716840-X

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Abstract:

We obtain estimates for certain sums of Fourier-Stieltjes (and hence also Fourier) coefficients of continuous functions $f$ of bounded variation in terms of the modulus of continuity of $f$. As a consequence of one of our results we obtain an improvement on a theorem of Zygmund on the absolute convergence of Fourier series of functions of bounded variation. We also consider absolutely continuous functions and show by examples that a number of the results we obtain are "best possible".

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