Improved Buckley's theorem on locally compact abelian groups

Victoria Paternostro and Ezequiel Rela

Vol. 299 (2019), No. 1, 171–189

DOI: 10.2140/pjm.2019.299.171

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 $A_{\infty }$ weights and provide a valid version of the “open property” for Muckenhoupt $A_p$ weights.

Keywords

locally compact abelian groups, reverse Hölder inequality, Muckenhoupt weights, maximal functions

Mathematical Subject Classification 2010

Primary: 42B25

Secondary: 43A70

Milestones

Received: 14 November 2017

Revised: 15 May 2018

Accepted: 17 July 2018

Published: 18 April 2019