Title

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

Journal Title

Proceedings of the American Mathematical Society

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