Reverse Hölder Property for Strong Weights and General Measures

CARLOS PÉREZ; EZEQUIEL RELA; TERESA LUQUE

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2017 vol. 27 p. 162 - 182

1050-6926

We present dimension-free reverse H"older inequalities for strong $A^*_p$ weights, $1le p < infty$. 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 H"older inequality for certain product measures. As a corollary we derive mixed $A_p^*-A_infty^*$ weighted estimates.