Abstract
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.
Recommended Citation
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
Department(s)
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)
1088-6826; 0002-9939
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 American Mathematical Society, All rights reserved.
Publication Date
01 Jan 1981
