On 𝐿¹ convergence of Fourier series with quasi-monotone coefficients

Garrett, J. W.; Rees, C. S.; Stanojević, Č. V.

doi:10.1090/S0002-9939-1978-0509250-5

On $L^{1}$ convergence of Fourier series with quasi-monotone coefficients
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by J. W. Garrett, C. S. Rees and Č. V. Stanojević PDF

Proc. Amer. Math. Soc. 72 (1978), 535-538 Request permission

Abstract:

For the class of Fourier series with quasi-monotone coefficients, it is proved that $\left \| {{s_n} - {\sigma _n}} \right \| = o(1),n \to \infty$, 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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