On unconditionality of fractional Rademacher chaos in symmetric spaces

S. V. Astashkin; K. V. Lykov

paper

On unconditionality of fractional Rademacher chaos in symmetric spaces

arXiv:2305.11478

Abstract

We study density estimates of an index set $A$ , under which unconditionality (or even a weaker property of the random unconditional divergence) of the corresponding Rademacher fractional chaos ${r_{j_{1}} (t) \cdot r_{j_{2}} (t) \cdot \dots \cdot r_{j_{d}} (t)}_{(j_{1}, j_{2}, \dots, j_{d}) \in A}$ in a symmetric space $X$ implies its equivalence in $X$ to the canonical basis in $ℓ_{2}$ . 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 $L_{M}$ .

to appear in Izv. RAN