关于 $\mathcal{A}_{p(\cdot)}$ 权的反 H"older 不等式及其关于矩阵权的应用
经典分析与常微分方程
2025-09-15 v2
摘要
本文证明了针对变量指数 Muckenhoupt 权 的反 H"older 不等式，这些权由第一作者、Fiorenza 和 Neugeabauer 引入。我们的所有估计都是定量的，显示指数函数对 特征的依赖性。作为应用，我们使用反 H"older 不等式证明矩阵 权（我们在前一篇论文中引入的）具有右开和左开属性。这一结果即使在标量情形下也是全新的。
引用
@article{arxiv.2411.12849,
title = {The reverse H\"older inequality for $\mathcal{A}_{p(\cdot)}$ weights with applications to matrix weights},
author = {David Cruz-Uribe and Michael Penrod},
journal= {arXiv preprint arXiv:2411.12849},
year = {2025}
}
备注
Minor typos corrected. We corrected the definition of the reverse Holder exponent r, as it was missing a $p_+$ power. The constant $C_*$ was missing a dependence on the Diening constant $C_D$. We removed the incorrect dependence on $d$ in Lemma 5.10. We clarified where the correct constant in Lemma 5.10 comes from by more clearly stating the constant in Proposition 5.8