Convergence in the mean of a class of \(N\)-dimensional trigonometric series (Q2720912)

Criteria for convergence in the mean of \(N\)-dimensional trigonometric series are proved under some conditions on the coefficients of these series. The given conditions depend essentially on the domain determining the partial sums of the series. Two domains are considered in this article -- the torus in \( R^N \) and the disk in \( R^2\). In particular, an analog of the well-known one-dimensional Sidon-Telyakovskij theorem [see \textit{S. A. Telyakovskij}, Math. Notes 14(1973), 742-748 (1974); translation from Mat. Zametki 14, 317-328 (1973; Zbl 0281.42011)] is proved in the case of convergence by disks.