Geodesic
On unconditional convergence with respect to systems of products of bases
Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 231-244

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Decisive conditions are established for unconditionality of expansions with respect to bases in spaces of functions of several variables. The properties of the multiple Haar and Franklin systems are studied. 
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     author = {G. E. Tkebuchava},
     title = {On unconditional convergence with respect to systems of products of bases},
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G. E. Tkebuchava. On unconditional convergence with respect to systems of products of bases. Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 231-244. http://geodesic.mathdoc.fr/item/SM_1994_77_1_a13/