Sufficient conditions for one-sided operators

In this article we give sufficient conditions on a pair of weight (w, v) for some one-sided operators to be bounded from Lp (vp) to Lp (wp). The operators we deal with include the one-sided fractional maximal operator and the one-sided singular integrals. For the first operator, necessary and sufficient conditions are known (see [8, 6]). These conditions usually amount to checking the boundedness of the operator on functions that are powers of the weights and are hard to check. Our conditions are of Ap type and are therefore easy to verify. Similar results for two-sided operators were obtained by C. Pérez in [9] and [10].