We analyze the possibility of decomposition of the series \( \sum {\frac{1}{k}\sin k\,x} \) in blocks such that the sum of the series formed by the moduli of these blocks belongs to the spaces L p [0 π] or to the spaces L p [0 π] with weight x −γ, γ< 1..
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 713–718, May, 2012.
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Telyakovskii, S.A. On the properties of blocks of terms of the series \( \sum {\frac{1}{k}\sin k\,x} \) . Ukr Math J 64, 816–822 (2012). https://doi.org/10.1007/s11253-012-0680-7
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DOI: https://doi.org/10.1007/s11253-012-0680-7