ABSTRACT
In this chapter we obtain extrapolation theorems for pairs of weights o: and (3 that satisfy the relation o: = vP (3, where v is a given positive function and o: and (3 belong to Ap. The extrapolation theorems obtained are motivated by the result of Steve Bloom [1] on the commutator of the Hilbert transform and are applied to commutators of V-Dini singular integral operators; see Theorem (3.7). Theorem (2.4), the extrapolation from r = oo, is a generalization of a result contained in [5], in the same way as Theorem (2.3) generalizes results of [7] and [3]. For notation and the general theory ofAp weights, we indicate [4], for instance. A result related to Theorem (2.3) for v = 1 was considered by F. J. Ruiz [8].
