On L^1-Convergence Of Rees-Stanojević's Sums With Coefficients From The Class K
Keywords:
Cosine sums, Conjugate Fejer kernel, $L^{1}$-convergence.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.Downloads
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