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.