Reverse Hölder Property for strong weights and general measures

Abstract

We present dimension-free reverse Hölder inequalities for strong $A_p^{\ast }$ weights, $1\le p<\infty$. We also provide a proof for the full range of local integrability of $A_1^{\ast }$ 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 $A_p^{\ast }-A_{\infty }^{\ast }$ weighted estimates.

To appear in Journal of Geometric Analysis

References in corpus (1)

• Weighted Solyanik estimates for the strong maximal function