SOME CHARACTERIZATIONS OF BMO 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, Mη] in Orlicz spaces LΦ(X) over spaces of homogeneous type X = (X, d, µ) when b belongs to BMO(X) spaces. We obtain some new characterizations for certain subclasses of BMO(X) spaces. © 2023 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.