Geodesic
On the series of absolute values of blocks of trigonometric series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 243-251

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Conditions of integrability with a power weight are obtained for the sums of series of absolute values of blocks of sine series and cosine series under certain special conditions imposed on the coefficients of these series. 
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     author = {S. A. Telyakovskii},
     title = {On the series of absolute values of blocks of trigonometric series},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {243--251},
     publisher = {mathdoc},
     volume = {284},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_284_a16/}
}
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S. A. Telyakovskii. On the series of absolute values of blocks of trigonometric series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 243-251. http://geodesic.mathdoc.fr/item/TM_2014_284_a16/