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