Title: On a structure theorem of doubling weights, Muckenhoupt Ap weights and reverse Holder weights.

Abstract: In this talk, I will introduce a way to construct an explicit family of measures on the real line that are p-adic doubling for any finite set of primes, however, not doubling. This part generalizes the work of Boylan, Mills and Ward in 2019 in a highly non-trivial way. As some applications, we apply these results to show analogous statements for the Muckenhoupt Ap weights and reverse Holder weights. The proofs involve an interplay among several geometric and number theoretic properties. This talk is based on a joint work with Tess Anderson.