Two-Weight Factorization

Our primary goal in this chapter is to define the appropriate analogs of A 1 weights and prove a “reverse factorization” property for pairs of weights that satisfy the A p bump conditions defined in Chapter 5. As we discussed in Chapter 2, reverse factorization is an essential tool in the proof of the Rubio de Francia extrapolation theorem; in the two-weight case these ideas play a similar but less direct role, as we will discuss in Chapter 7.