Some Characterizations of BMO Spaces via Commutators in Orlicz Spaces on Stratified Lie Groups

In the paper we study the fractional maximal commutators M-b,M- alpha and the commutators of the fractional maximal operator [b, M-alpha] in the Orlicz spaces L-Phi(G) on any stratified Lie group G. We give necessary and sufficient conditions for the boundedness of the operators M-b,M-alpha and [b, M-alpha] on Orlicz spaces L-Phi (G) when b belongs to BMO(G) spaces, whereby some new characterizations for certain subclasses of BMO(G) spaces are obtained.