New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderon reproducing formulae and the Plancherel-Polya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p; q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p; q≤ 1 on spaces of homogeneous type. Moreover, atomic decompositions of these new spaces are also obtained. All the results of this paper are new even for Rn.