Rademacher functions in weighted symmetric spaces

TL;DR

This paper investigates the behavior of Rademacher functions within weighted symmetric spaces, characterizing weights that ensure bounded Rademacher projections using multiplicator space properties.

Contribution

It provides a new description of weights for which the Rademacher orthogonal projection is bounded in weighted symmetric spaces, utilizing multiplicator space concepts.

Findings

Characterization of weights w for bounded Rademacher projections

Use of Rademacher multiplicator space properties

Extension of symmetric space analysis to weighted contexts

Abstract

The closed span of Rademacher functions is investigated in the weighted spaces X(w), where X is a symmetric space on [0,1] and w is a positive measurable function on [0,1]. By using the notion and properties of the Rademacher multiplicator space of a symmetric space, we give a description of the weights w for which the Rademacher orthogonal projection is bounded in X(w).