A new quantitative two weight theorem for the Hardy-Littlewood maximal operator

Abstract

A quantitative two weight theorem for the Hardy-Littlewood maximal operator is proved, improving the known ones. As a consequence, a new proof of the main results in papers by Hyt¨onen and the first author and Hyt¨onen, the first author and Rela is obtained which avoids the use of the sharp quantitative reverse Holder inequality for A∞ proved in those papers. Our results are valid within the context of spaces of homogeneous type without imposing the non-empty annuli condition.