Geodesic
RUC Bases and the Olevskii System
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 566-579.

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In this paper, we study the RUC-basis properties of the Olevskii system in rearrangement-invariant spaces. In particular, it is proved that the Olevskii system forms an RUC basis in $L_p[0,1]$ if and only if $2\le p\infty$. 
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K. S. Kazarian; E. M. Semenov. RUC Bases and the Olevskii System. Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 566-579. http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a5/

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