Sufficient conditions for one-sided operators

In this article we give sufficient conditions on a pair of weights (w, v)fo r some one-sided operators to be bounded from L-P(v(P)) to L-P(w(P)). The o perators we deal with include the one-sided fractional maximal operator and the one-sided singular integrals. For the first operator; necessary and su fficient conditions are known (see [8, 6]). These conditions usually amount to checking the boundedness of the operator on functions that are powers o f the weights and are hard to check Our conditions are of Ap type and are t herefore easy to verify Similar results for two-sided operators were obtain ed by C. Perez in [9] and [10].