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On $ L\sp{1}$ convergence of Fourier series with quasi-monotone coefficients


Authors: J. W. Garrett, C. S. Rees and Č. V. Stanojević
Journal: Proc. Amer. Math. Soc. 72 (1978), 535-538
MSC: Primary 42A20
DOI: https://doi.org/10.1090/S0002-9939-1978-0509250-5
MathSciNet review: 509250
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Abstract: For the class of Fourier series with quasi-monotone coefficients, it is proved that $ \left\Vert {{s_n} - {\sigma _n}} \right\Vert = o(1),n \to \infty $, if and only if $ {a_n}\lg n = o(1),n \to \infty $. This generalizes a theorem for monotone coefficients and provides a new proof for a result due to Telyakovskii and Fomin.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509250-5
Keywords: $ {L^1}$-convergence of Fourier series, Fejér sums
Article copyright: © Copyright 1978 American Mathematical Society