Reverse Hölder Property for Strong Weights and General Measures

Abstract

We present dimension-free reverse Hölder inequalities for strong Ap∗ weights, 1 ≤ p< ∞. We also provide a proof for the full range of local integrability of A1∗ 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= ∞, we also provide a reverse Hölder inequality for certain product measures. As a corollary we derive mixed Ap∗-A∞∗ weighted estimates.