It is shown that the Fomin class FP (1
< 2) is a subclass of C ∩ B V, where C is the Garrett-Stanojevic class and B V the class of sequences of bounded variation. Wider classes of Fourier and Fourier-Stieltjes series are found for which an lg n - o(1), n → ∞, is a necessary and sufficient condition for L1-convergence. For cosine series with coefficients in B V and n∆an = 0(1), n → ∞, necessary and sufficient integrability conditions are obtained. © 1981 American Mathematical Society.
Č. V. Stanojevic, "Classes Of L¹-convergence Of Fourier And Fourier-stieltjes Series," Proceedings of the American Mathematical Society, vol. 82, no. 2, pp. 209 - 215, American Mathematical Society, Jan 1981.
The definitive version is available at https://doi.org/10.1090/s0002-9939-1981-0609653-4
Mathematics and Statistics
Keywords and Phrases
Integrability of cosine series; L -convergence of Fourier series and Fourier-Stieltjes series 1
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 1981