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AbstractIn this paper we study the relationship between one-sided reverse Hölder classes RHr+ and the Ap+ classes. We find the best possible range of RHr+ to which an A1+ weight belongs, in terms of the A1+ constant. Conversely, we also find the best range of Ap+ to which a RH∞+ weight belongs, in terms of the RH∞+ constant. Similar problems for Ap+, 1
RHr+, 1<r<∞ are solved using factorization.