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

In the paper we study the fractional maximal commutators Mb,α and the commutators of the fractional maximal operator [b, Mα] in the Orlicz spaces LΦ(G) on any stratified Lie group G. We give necessary and sufficient conditions for the boundedness of the operators Mb,α and [b, Mα] on Orlicz spaces LΦ(G) when b belongs to BMO(G) spaces, whereby some new characterizations for certain subclasses of BMO(G) spaces are obtained. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.