Rademacher functions in weighted symmetric spaces

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).