Sharp Lp bounds for the centered Hardy-Littlewood maximal function on hyperbolic spaces 

We will provide sharp weak type estimates for the Hardy-Littlewood maximal operator in the context of Gromov hyperbolic metric measure spaces, which satisfy a locally doubling condition and the measures of balls grows exponentially for large radii. This result generalizes previous results on symmetric spaces of non compact type and rank 1, Damek-Ricci spaces, and Riemannian manifolds of pinched negative curvature. This is a joint work with S. Meda and F. Santagati.