Abstract
It is proved that if the Fourier coefficients (an) of /E L!(0, ir) satisfy (*)L" kp\Aan\p = o(l), for some 1
< 2, then \\sn- f\\ = o(l), if and only if a" lg n * o(l). For cosine trigonometric series with coefficients of bounded variation and satisfying (*) it is proved that a necessary and sufficient condition for the series to be a Fourier series is (an) E 6, where G is the Garrett-Stanojevic [4] class. © 1982 American Mathematical Society.
Recommended Citation
R. Bojan1c and C. V. Stanojevic, "A Class Of L¹-convergence," Transactions of the American Mathematical Society, vol. 269, no. 2, pp. 677 - 683, American Mathematical Society, Jan 1982.
The definitive version is available at https://doi.org/10.1090/S0002-9947-1982-0637717-3
Department(s)
Mathematics and Statistics
Keywords and Phrases
Integrability of cosine series; Ll-convergence of Fourier series
International Standard Serial Number (ISSN)
0002-9947
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 1982
