Geodesic
Haar systems and~some results on~the~basis in~a~martingale space with mixed norm
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 623-626

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For martingale spaces with mixed norm defined with respect to diadic flow of $\sigma$-algebras, we find a condition on summation characteristics, which implies no unconditional basis in these spaces (a generalization of the classical result of Pelczynski proved for $L_1$-spaces). In these spaces (under other conditions on characteristics) generalized Haar systems are considered; the test of the existence of an unconditional basis in terms of the Paley function is obtained and the convergence theorem for almost all choices of signs is proved.
Mots-clés : martingale
Keywords: mixed norm, diadic flow, Haar system, unconditional basis. 
@article{TVP_1997_42_3_a13,
     author = {I. V. Pavlov},
     title = {Haar systems and~some results on~the~basis in~a~martingale space with mixed norm},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {623--626},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a13/}
}
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I. V. Pavlov. Haar systems and~some results on~the~basis in~a~martingale space with mixed norm. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 623-626. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a13/