Reverse Hölder Property for strong weights and general measures

2015/12/03 by Teresa Luque, Carlos Pérez, Luque, Teresa +3
Mathematics · Medicine · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.1512.01112

Abstract

We present dimension-free reverse Hölder inequalities for strong A^*_p 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 A_p^*-A_∞^* weighted estimates.

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