Naslov
Generalization on some theorems of L1-convergence of certain trigonometric series

Autori
Tomovski, Živorad

Izvornik
Tamkang Journal of Mathematics (0049-2930) 39 (2008), 1; 63-74

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
L1-convergence; trigonometric series; r-th derivatives of Fourier series; Wang-Telyakovskii class; Sheng class; Fomin class.

Sažetak
It this paper we study L1 - convergence of the r-th derivatives of Fourier series with complex-valued coefficients. Namely new necessary - sufficient conditions for L1 - 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 $(BV)^\sigma_r, \sigma > 0, r=0, 1, 2, \cdots$ we generalize also the theorem proved by Garrett, Rees and Stanojević in[5]. Finally, for $\sigma = 1$ some corollaries of this theorem are given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA