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.

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