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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.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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