  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).

Functional Analysis