On the properties of blocks of terms of the series $\sum \cfrac1k \sin kx$

• Date: 2012
• Main Authors: Telyakovskii, S. A., Теляковский, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2610
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the decomposability of the series $\sum \cfrac1k \sin kx$ into blocks such that the sum of the series formed of the moduli of these blocks belongs to the spaces $L^p[0, \pi]$ or the spaces $L^p[0, \pi]$ with weight $x^{-\gamma},\quad \gamma < 1$.