Endpoint estimates and sparse domination in nonhomogeneous trees

We prove endpoint and sparse-like bounds for Bergman projectors on nonho-mogeneous, radial treesXthat model manifolds with possibly unbounded geometry. Thenatural Bergman measures onXmay fail to be doubling, and even locally doubling, withrespect to the right metric in our setting. Weighted consequences of our sparse domina-tion results are also considered, and are in line with the known results in the disk. Ourendpoint results are partly a consequence of a new Calder ́on-Zygmund theory for discrete,non-locally doubling metric spaces.