Improved Buckley's theorem on locally compact abelian groups

Abstract

We present sharp quantitative weighted norm inequalities for the Hardy- Littlewood maximal function in the context of locally compact abelian groups, obtaining an improved version of the so-called Buckley's theorem. On the way, we prove a precise reverse Hölder inequality for Muckenhoupt A∞ weights and provide a valid version of the "open property" for Muckenhoupt Ap weights.