SOME CLASSES OF \(L^1\)-CONVERGENCE OF FOURIER SERIES

Abstract

We study here \(L^1\)-convergence of a trigonometric series, i.e. the extension is made for the Č. V. Stanojević and V. B. Stanojević theorem [5] and also for the theorem proved by the author in[7]. Namely, the new necessary-sufficient conditions for \(L^1\)-convergence of Fourier series with \(\delta\)-quasi-monotone coefficients are obtained.

Then it is verified that the three classes of Fourier coefficients defined by Fomin; Č. V. Stanojević, V. B. Stanojević and the author of the present note, are identical.