Belov, A. S. Some properties of the sum of the moduli of the terms of a grouped trigonometric series. (English. Russian original) Zbl 1268.42004 Sb. Math. 203, No. 6, 798-825 (2012); translation from Mat. Sb. 203, No. 6, 35-62 (2012). Interesting results concerning trigonometric series grouped in a certain way and such that the coefficients are monotonic in each group are obtained in this paper. In particular, necessary and sufficient conditions for this sum to lie in the spaces \(L^p\) are obtained. Reviewer: Martin Grigoryan (Yerevan) Cited in 2 Documents MSC: 42A20 Convergence and absolute convergence of Fourier and trigonometric series 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) Keywords:absolute convergence; grouped trigonometric series PDFBibTeX XMLCite \textit{A. S. Belov}, Sb. Math. 203, No. 6, 798--825 (2012; Zbl 1268.42004); translation from Mat. Sb. 203, No. 6, 35--62 (2012) Full Text: DOI