Rademacher chaos in symmetric spaces

TL;DR

This paper establishes conditions under which Rademacher chaos spaces are equivalent to l_2 basis and explores their complementability, highlighting the limits of exponential integrability in these spaces.

Contribution

It provides necessary and sufficient conditions for Rademacher chaos to be equivalent to l_2 and for the subspace's complementability, advancing understanding of their structure.

Findings

Criteria for equivalence to l_2 basis

Conditions for subspace complementability

Unimprovability of exponential integrability

Abstract

Necessary and sufficient conditions for the equivalence of the Rademacher chaos to the canonical basis of l_2 and also for the complementability of the corresponding generated subspace are derived. In particular, we obtain the unimprovability of the exponential integrability of functions from this space.