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arXiv · 2305.11478

On unconditionality of fractional Rademacher chaos in symmetric spaces

S. V. Astashkin·K. V. Lykov
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Abstract

We study density estimates of an index set $\mathcal{A}$, under which unconditionality (or even a weaker property of the random unconditional divergence) of the corresponding Rademacher fractional chaos $\{r_{j_1}(t)\cdot r_{j_2}(t)\cdot\dots\cdot r_{j_d}(t)\}_{(j_1,j_2,\dots,j_d)\in \mathcal{A}}$ 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 equivalent to the fact that a certain exponential Orlicz space embeds into $L_M$.

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S. V. Astashkin, K. V. Lykov. 2023-05-19. On unconditionality of fractional Rademacher chaos in symmetric spaces. https://arxiv.org/abs/2305.11478

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