On weighted integrability of trigonometric series and L1-convergence of fourier series
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.
Document Type
Article
DOI
https://doi.org/10.1090/S0002-9939-1986-0813809-X
Keywords
Integrability of trigonometric series, L -convergence of Fourier series 1, Regularly varying sequences, Slowly varying functions
Publication Date
1-1-1986
Recommended Citation
Bray, William O., and Časlav V. Stanojević. "On weighted integrability of trigonometric series and ��¹-convergence of Fourier series." Proceedings of the American Mathematical Society 96, no. 1 (1986): 53-61.
Journal Title
Proceedings of the American Mathematical Society
