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

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-Hölder continuity conditions and $1<p_{-}\le p_{+}<\infty$. Our results generalize to spaces of homogeneous type the analogous results in Euclidean space proved by Cruz-Uribe, Fiorenza and Neugebuaer (2012).

References in corpus (1)

• Dyadic cubes in spaces of homogeneous type