Geodesic
The Hardy-Littlewood theorem for the cosine series in a symmetric space
Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 241-246.

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For a wide class of functional spaces we obtain a necessary and sufficient condition on a space that guarantees a Hardy–Littlewood type of assertion about whether the sum of a cosine series with monotonic coefficients belongs to a functional space, e.g., $L_p$ ($p>1$). As examples we consider Lorentz spaces, Marcinkiewicz spaces, Orlicz spaces, and $L_p$ spaces. 
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     author = {V. A. Rodin},
     title = {The {Hardy-Littlewood} theorem for the cosine series in a symmetric space},
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     publisher = {mathdoc},
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     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a8/}
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V. A. Rodin. The Hardy-Littlewood theorem for the cosine series in a symmetric space. Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 241-246. http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a8/