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Abstract
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study its weighted boundedness. Motivated by the weighted boundedness of the Hardy-Littlewood maximal studied by Antezana and Ombrosi in [1], we give conditions for the weak type and strong type estimate for fractional maximal. Also, we present examples of weights for which the fractional maximal operator satisfies weak type (p,q) inequality but strong type (p,q) inequality fails.
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