A weighted Khintchine inequality

i=1 ai 1/2 , for every (ai) ∈ l, where (ri) are the Rademacher functions, that is, ri(t) := sign sin(2πt), t ∈ [0, 1], i ∈ N. A weighted version of the above inequality was recently proved in [18]. Namely, let w be a weight satisfying the following conditions (a) for some q > p we have w ∈ L([0, 1]); (b) the support of w satisfies m(supp(w)) > 2/3. Then there exist constants C1, C2 > 0, depending on p and w, such that for every a = (ai) ∈ l