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 $2\le p\infty$. 
@article{MZM_2004_75_4_a5,
     author = {K. S. Kazarian and E. M. Semenov},
     title = {RUC {Bases} and the {Olevskii} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {566--579},
     publisher = {mathdoc},
     volume = {75},
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     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a5/}
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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/