On weighted integrability of trigonometric series and L1-convergence of fourier series
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  is proved. Our result is an excludedďcase in more classical results (see ) and also generalizes a result of G. A. Fomin . Also a result of Fomin and Telyakovskii  concerning L1-convergence of Fourier series is generalized. Both theorems make use of a generalized notion of quasi-monotone sequences. © 1986 American Mathematical Society.
Integrability of trigonometric series, L -convergence of Fourier series 1, Regularly varying sequences, Slowly varying functions
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.
Proceedings of the American Mathematical Society