Boundedness of maximal operators and maximal commutators on non-homogenous spaces

Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the Lp boundedness of the maximal commutator with RBMO function