Weighted norm inequalities for the maximal operator on \Lpp over spaces of homogeneous type

2020/07/21 by Cruz-Uribe, David, Cummings, Jeremy · 1 citation
#42B25 #46A80 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.10864

Abstract

Given a space of homogeneous type (X,μ,d), we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces L^\pp. We prove that the variable Muckenhoupt condition \App is necessary and sufficient for the strong type inequality if \pp satisfies log-Hölder continuity conditions and 1 < p_- ≤ p₊ < ∞. Our results generalize to spaces of homogeneous type the analogous results in Euclidean space proved by Cruz-Uribe, Fiorenza and Neugebuaer (2012).

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• The maximal function on spaces of homogeneous type, or adjacent dyadic cubes do good

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