Abstract
Result concerning integrability of f(x)L(l/x)(g(x)L(l/x)), where f(x)(g(x)) is the pointwise limit of certain cosine (sine) series and L(•) is slowly vary in the sense of Karamata [5] is proved. Our result is an excludedďcase in more classical results (see [4]) and also generalizes a result of G. A. Fomin [1]. Also a result of Fomin and Telyakovskii [6] concerning L1-convergence of Fourier series is generalized. Both theorems make use of a generalized notion of quasi-monotone sequences. © 1986 American Mathematical Society.
Recommended Citation
W. O. Bray and C. V. Stanojević, "On Weighted Integrability Of Trigonometric Series And L¹-convergence Of Fourier Series," Proceedings of the American Mathematical Society, vol. 96, no. 1, pp. 53 - 61, American Mathematical Society, Jan 1986.
The definitive version is available at https://doi.org/10.1090/S0002-9939-1986-0813809-X
Department(s)
Mathematics and Statistics
Keywords and Phrases
Integrability of trigonometric series; L -convergence of Fourier series 1; Regularly varying sequences; Slowly varying functions
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 1986
