Weighted norm inequalities for the maximal function on spaces of homogeneous type

A characterization is obtained for weight function v for which the Hardy-Littlewood operator relative to a metric d is bounded from L^P(X, wdμ) to L^P(X, vdμ) for some nontrivial w, where (X, d, μ) is a space of homogeneous type. Supported by Natural Science Foundation of China.