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<p>A series of long-standing questions in harmonic analysis ask whether the intersection of all prime “<i>p</i>-adic versions” of an object, such as a doubling measure or a Muckenhoupt or reverse Hölder weight, recovers the full object. Investigation into these questions was reinvigorated in 2019 by work of Boylan–Mills–Ward, culminating in showing that this recovery fails for a finite intersection in work of Anderson–Bellah–Markman–Pollard–Zeitlin. Via generalizing a new number theoretic construction therein, we answer these questions.</p>

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Infinite intersections of doubling measures, weights, and function classes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月31日

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  • Theresa C. Anderson,
  • David Philips,
  • Anastasiia Rudenko,
  • Kevin You

摘要

A series of long-standing questions in harmonic analysis ask whether the intersection of all prime “p-adic versions” of an object, such as a doubling measure or a Muckenhoupt or reverse Hölder weight, recovers the full object. Investigation into these questions was reinvigorated in 2019 by work of Boylan–Mills–Ward, culminating in showing that this recovery fails for a finite intersection in work of Anderson–Bellah–Markman–Pollard–Zeitlin. Via generalizing a new number theoretic construction therein, we answer these questions.