A Structure Theorem on Intersections of General Doubling Measures and Its Applications
Abstract
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are -adic and -adic doubling for any distinct primes and , yet not doubling, and we apply these results to show analogous statements about the reverse H\"older and Muckenhoupt classes of weights. The proofs involve a delicate interplay among several geometric and number theoretic properties.
Cite
@article{arxiv.2009.03875,
title = {A Structure Theorem on Intersections of General Doubling Measures and Its Applications},
author = {Theresa C. Anderson and Bingyang Hu},
journal= {arXiv preprint arXiv:2009.03875},
year = {2023}
}
Comments
46 pages, 9 figures. Extending construction to a finite set of primes is a difficult problem and the short extension claimed here does not work. All results continue to hold for two primes. The final version of this article has just appeared in IMRN, thus the arXiv version has not been updated. Title updated to match published version