#### Vol. 299, No. 1, 2019

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Improved Buckley's theorem on locally compact abelian groups

### Victoria Paternostro and Ezequiel Rela

Vol. 299 (2019), No. 1, 171–189
##### 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
Primary: 42B25
Secondary: 43A70
##### Milestones
Received: 14 November 2017
Revised: 15 May 2018
Accepted: 17 July 2018
Published: 18 April 2019
##### Authors
 Victoria Paternostro Departamento de Matemática, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Buenos Aires Argentina Ezequiel Rela Departamento de Matemática, Facultad de Ciencias Exactes y Naturales Universidad de Buenos Aires Buenos Aires Argentina