On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K

Abstract

In this paper are considered the modified cosine sums introduced by Rees and Stanojević  with coefficients from the class K. In addition, it is proved that the condition $\lim_{n\to \infty}|a_{n+1}|\log n= 0$ is a necessary and sufficient condition for the $L^{1}$-convergence of the cosine series. Also, an open problem about $L^{1}$-convergence for the $r-th$ derivative  of the cosine series is presented.

Keywords

• Cosine sums
• Conjugate Fejer kernel
• $L^{1}$-convergence.