2017
Том 69
№ 7

All Issues

On the properties of blocks of terms of the series $\sum \cfrac1k \sin kx$

Telyakovskii S. A.

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Abstract

We investigate the decomposability of the series $\sum \cfrac1k \sin kx$ into blocks such that the sum of the series formed of the moduli of these blocks belongs to the spaces $L^p[0, \pi]$ or the spaces $L^p[0, \pi]$ with weight $x^{-\gamma},\quad \gamma < 1$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 816-822.

Citation Example: Telyakovskii S. A. On the properties of blocks of terms of the series $\sum \cfrac1k \sin kx$ // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 713-718.

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