Improved Buckley’s theorem on locally compact abelian groups

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.

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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

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

Vol. 299, No. 1, 2019

Victoria Paternostro and Ezequiel Rela

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors