A Structure Theorem on Intersections of General Doubling Measures and Its Applications.

In this paper, we construct an explicit family of measures that are $p$ -adic doubling for any given pair of primes, yet not doubling. This generalizes the construction by Boylan, Mills, and Ward on a structure theorem on the intersection of dyadic doubling measures and tri-adic doubling measures. As some byproducts, we apply these results to show analogous statements about the reverse Hölder and Muckenhoupt $A_p$ classes of weights. [ABSTRACT FROM AUTHOR]