GENERALIZATION ON SOME THEOREMS OF L-1-CONVERGENCE OF CERTAIN TRIGONOMETRIC SERIES

In this paper we study L-1-convergence of the r-th derivatives of Fourier series with complex-valued coefficients. Namely new necessary-sufficient conditions for L-1-convergence of the r-th derivatives of Fourier series are given. These results generalize corresponding theorems proved by several authors (see [7], [10], [13], [19]). Applying the Wang-Telyakovskii class (BV)(r)(sigma), sigma > 0, r = 0, 1, 2, ... we generalize also the theorem proved by Garrett, Rees and Stanojevic in [5]. Finally, for sigma = 1 some corollaries of this theorem are given.