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arXiv · 2009.03875

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

Theresa C. Anderson·Bingyang Hu
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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 $p$-adic and $q$-adic doubling for any distinct primes $p$ and $q$, yet not doubling, and we apply these results to show analogous statements about the reverse Hölder and Muckenhoupt $A_p$ classes of weights. The proofs involve a delicate interplay among several geometric and number theoretic properties.

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BibTeXRIS

Theresa C. Anderson, Bingyang Hu. 2023-09-21. A Structure Theorem on Intersections of General Doubling Measures and Its Applications. https://arxiv.org/abs/2009.03875

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