The Structure of Weight and Function Classes With Coprime Bases

Abstract In a recent work of Anderson and Hu, the authors constructed a measure that was p-adic and q-adic doubling, for any primes p and q, yet not doubling. This work relied heavily on a developed number theory framework. Here we develop this framework further, which yields a measure that is m-adic and n-adic doubling for any coprime $m,n$, yet not doubling. Additionally, we show several new applications to the intersection of weight and function classes.