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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On certain sums of Fourier-Stieltjes coefficients


Author: J. B. Twomey
Journal: Trans. Amer. Math. Soc. 280 (1983), 611-621
MSC: Primary 42A16; Secondary 42A28
DOI: https://doi.org/10.1090/S0002-9947-1983-0716840-X
MathSciNet review: 716840
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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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DOI: https://doi.org/10.1090/S0002-9947-1983-0716840-X
Keywords: Fourier-Stieltjes coefficients, coefficient estimates, functions of bounded variation, absolutely continuous functions, modulus of continuity, absolutely convergent Fourier series
Article copyright: © Copyright 1983 American Mathematical Society