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Abstract
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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
weights and provide a valid version of the “open property” for Muckenhoupt
weights.
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Keywords
locally compact abelian groups, reverse Hölder inequality,
Muckenhoupt weights, maximal functions
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Mathematical Subject Classification 2010
Primary: 42B25
Secondary: 43A70
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Milestones
Received: 14 November 2017
Revised: 15 May 2018
Accepted: 17 July 2018
Published: 18 April 2019
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