Reverse Hölder Property for Strong Weights and General Measures

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• 作者：Teresa Luque ; Carlos Pérez ; Ezequiel Rela
• 关键词：Reverse Hölder inequality ; Muckenhoupt weights ; Maximal functions ; Multiparameter harmonic analysis
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：162-182
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

We present dimension-free reverse Hölder inequalities for strong \(A^*_p\) weights, \(1\le p < \infty \). We also provide a proof for the full range of local integrability of \(A_1^*\) weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For \(p=\infty \), we also provide a reverse Hölder inequality for certain product measures. As a corollary we derive mixed \(A_p^*-A_\infty ^*\) weighted estimates.