CHARACTERIZATIONS OF LIPSCHITZ FUNCTIONS VIA THE COMMUTATORS OF MAXIMAL FUNCTION IN ORLICZ SPACES ON STRATIFIED LIE GROUPS

We give necessary and sufficient conditions for the boundedness of the maximal commutators Mb, the commutators of the maximal operator [b, M] and the commutators of the sharp maximal operator [b,M-double dagger] in Orlicz spaces L-Phi(G) on any stratified Lie group G when b belongs to Lipschitz spaces.Lambda(beta) (G). We obtain some new characterizations for certain subclasses of Lipschitz spaces Lambda(beta)(G)