Fractional Maximal operator in hyperbolic spaces
Abstract
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of 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 provide examples of weights for which the fractional maximal operator satisface weak type (p,q) inequality but strong type (p,q) inequality fails.
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