ON Ap-Aq WEIGHTED ESTIMATES FOR MAXIMAL OPERATORS

The paper is devoted to the study of sharp versions of mixed A(p)-A(q) weighted estimates for the dyadic maximal function M-d on R-n. For given parameters 1 < p < infinity and 1 <= q <= infinity, if a weight w satisfies Muckenhoupt's condition A(p), then we have the sharp A(p)-A(q) bound parallel to M-d parallel to(Lp(w)-> Lp(w)) <= p(1+1/p)/p - 1 (q/q - 1)((q-1)/p) [w](Ap)(1/p)[w(1/(1-p))](Aq)(1/p) (for q is an element of {1, infinity}, the constant is understood as an appropriate limit). Actually, a wider class of related sharp two-weight estimates for M-d is established. The results hold true in a more general context of maximal operators on probability spaces associated with a tree-like structure.