Infinite intersections of doubling measures, weights, and function classes
Classical Analysis and ODEs
2024-09-30 v1 Number Theory
Abstract
A series of longstanding questions in harmonic analysis ask if the intersection of all prime ``-adic versions" of an object, such as a doubling measure, or a Muckenhoupt or reverse H\"older 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.
Keywords
Cite
@article{arxiv.2409.18230,
title = {Infinite intersections of doubling measures, weights, and function classes},
author = {Theresa C. Anderson and David Phillips and Anastasiia Rudenko and Kevin You},
journal= {arXiv preprint arXiv:2409.18230},
year = {2024}
}