Geodesic
General Franklin system as a~basis in~$B^1[0,1]$
Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1120-1137

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For a general Franklin system $\{f_n\}_{n=0}^{\infty}$ generated by an admissible sequence $\mathcal T$, we obtain necessary and sufficient conditions on $\mathcal T$ under which the corresponding system is a basis or an unconditional basis in $B^1[0,1]$.
Keywords: general Franklin system, basis, unconditional basis, spaces $B^1$, $H^1$. 
@article{IM2_2014_78_6_a4,
     author = {G. G. Gevorkyan},
     title = {General {Franklin} system as a~basis in~$B^1[0,1]$},
     journal = {Izvestiya. Mathematics },
     pages = {1120--1137},
     publisher = {mathdoc},
     volume = {78},
     number = {6},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a4/}
}
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G. G. Gevorkyan. General Franklin system as a~basis in~$B^1[0,1]$. Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1120-1137. http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a4/