Abstract
This paper presents a survey of results on properties of series composed of the moduli of blocks of trigonometric series. The following questions are addressed: convergence, uniform convergence, and membership of the sum of series to L p and to weighted L p spaces. First results in this area pertaining to similar series for the Walsh system are put forward.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 209–216, 2013.
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Telyakovskii, S.A. Series Formed by the Moduli of Blocks of Terms of Trigonometric Series. A Survey. J Math Sci 209, 152–158 (2015). https://doi.org/10.1007/s10958-015-2492-4
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DOI: https://doi.org/10.1007/s10958-015-2492-4