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

In this paper we obtain necessary and sufficient conditions for the boundedness of the fractional maximal commutators Mb,α and the commutators of the fractional maximal operator [b,Mα] in Orlicz spaces L(G) on any stratified Lie group G when b belongs to Lipschitz spaces (G). We obtain some new characterizations for certain subclasses of Lipschitz spaces(G). © 2025 Elsevier B.V., All rights reserved.