On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

• Date: 2008
• Main Authors: Ivashchuk, O. V., Zaderei, P. V., Pelagenko, E. N., Іващук, О. В., Задерей, П. В., Пелагенко, Є. Н.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3177
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the trigonometric series $$\sum_{k=0}^{\infty}a_k\sum_{l\in kV \setminus (k-1)V}e^{i(l, x)}, \quad a_k\rightarrow 0,\quad k\rightarrow \infty,$$ given on $[-\pi, \pi)^m$, where $V$ is some polyhedron in $R^m$, we prove that the inequality $$\int\limits_{T^m}\left|\sum^{\infty}_{k=0} a_k \sum_{l\...