倍增量的任意有限交叉及其应用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-07-04 DOI:10.1016/j.jfa.2024.110573

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引用次数: 0

摘要

我们在分析领域的一个民间猜想上取得了重大进展，在实线上构造了一种度量，对于任何 n∈N 的有限列表，它在所有 n-adic 间隔上都是加倍的，但总体上却不是加倍的。特别是，我们通过使用一系列实质性的新思想，扩展了该领域以前的成果，包括博伊兰-米尔斯-沃德和安德森-胡的成果。此外，我们还提供了反向赫尔德权重、Ap 权重、哈代空间、BMO 和 VMO 函数类的几个非难应用，并将我们的结果与整个数论的关键原理和猜想联系起来。

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Arbitrary finite intersections of doubling measures and applications

We make major progress on a folkloric conjecture in analysis by constructing a measure on the real line which is doubling on all n-adic intervals for any finite list of $n \in N$ , yet not doubling overall. In particular, we extend previous results in the area, including those of Boylan-Mills-Ward and Anderson-Hu, by using a wide array of substantially new ideas. In addition, we provide several nontrivial applications to reverse Hölder weights, $A_{p}$ weights, Hardy spaces, BMO and VMO function classes, and connect our results with key principles and conjectures across number theory.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis