BMO on spaces of homogeneous type: a density result on C-C spaces

In the general setting of a space of homogeneous type endowed with an Ahlfors regular measure, we introduce the Banach spaces BMO and VMO defined through suitable cubes, and we prove that these spaces are topologically equivalent to the standard ones usually defined by means of balls. Through this fact we extend a known result of Sarason showing that C1 is locally dense in VMO in the setting of Carnot-Carathéodory metric spaces related to a family of free Hörmander vector fields X1;...;Xq.