SOME CHARACTERIZATIONS OF <i>BMO</i> SPACES VIA COMMUTATORS OF FRACTIONAL MAXIMAL OPERATOR IN ORLICZ SPACES OVER SPACES OF HOMOGENEOUS TYPE

We give the necessary and sufficient conditions for the boundedness of the commutators of the fractional maximal operator [b, M-eta] in Orlicz spaces L-Phi(X) over spaces of homogeneous type X = (X, d, mu) when b belongs to BMO(X) spaces. We obtain some new characterizations for certain subclasses of BMO(X) spaces.