Geodesic
On unconditionality of fractional Rademacher chaos in symmetric spaces
Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 1-17

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We study density estimates of an index set $\mathcal{A}$ under which the unconditionality (or even the weaker property of random unconditional divergence) of the corresponding Rademacher fractional chaos $\{r_{j_1}(t) \cdot r_{j_2}(t) \cdots r_{j_d}(t)\}_{(j_1,j_2,\dots,j_d) \in \mathcal{A}}$ in a symmetric space $X$ implies its equivalence in $X$ to the canonical basis in $\ell_2$. In the special case of Orlicz spaces $L_M$, unconditionality of this system is also shown to be equivalent to the fact that a certain exponential Orlicz space embeds into $L_M$.
Keywords: Rademacher functions, Rademacher chaos, symmetric space, combinatorial dimension, unconditional convergence. 
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     title = {On unconditionality of fractional {Rademacher} chaos in symmetric spaces},
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S. V. Astashkin; K. V. Lykov. On unconditionality of fractional Rademacher chaos in symmetric spaces. Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/IM2_2024_88_1_a0/