BMO FUNCTIONS IN SPACES OF HOMOGENEOUS TYPE

In this paper, we proved the following fact elementarily and easily. Let f be a functionon the space X of homogeneous type such thatwhere k∈Z, （log）is the repetition of logarithm by k times, and S runs through allspheres in X, then f∈BMO. Consequently, an analogue of Baernstein’s theorem was estab-lished on n-real and n-complex spheres.