Geodesic
Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients
Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1617-1631

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The Hardy-Littlewood theorem is established for trigonometric series with $\alpha$-monotone coefficients. Inequalities of Hardy-Littlewood kind are proved. Examples of series demonstrating that the results obtained are sharp are constructed. Bibliography: 15 titles.
Keywords: generalized monotone coefficients, Hardy-Littlewood theorem. 
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     author = {M. I. Dyachenko and E. D. Nursultanov},
     title = {Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients},
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M. I. Dyachenko; E. D. Nursultanov. Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients. Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1617-1631. http://geodesic.mathdoc.fr/item/SM_2009_200_11_a2/