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Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot )}$ over a space of homogeneous type $(X,d,\mu )$ if and only if it is bounded on its dual space $L^{p’(\cdot )}$, where $1/p(x)+1/p’(x)=1$ fo