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arXiv · 2007.10864

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

David Cruz-Uribe·Jeremy Cummings
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Abstract

Given a space of homogeneous type $(X,\mu,d)$, 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-H\"older continuity conditions and $1 < p_- \leq p_+ < \infty$. 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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David Cruz-Uribe, Jeremy Cummings. 2020-07-21. Weighted norm inequalities for the maximal operator on $\Lpp$ over spaces of homogeneous type. https://arxiv.org/abs/2007.10864

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