Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 716840
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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".

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42A16, 42A28

Retrieve articles in all journals with MSC: 42A16, 42A28

Additional Information

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