Characterizations of Lipschitz functions via the commutators of fractional maximal function in total Morrey spaces on stratified Lie groups

The aim of this paper is to study the fractional maximal commutators Mb,α and the commutators of the fractional maximal operator [b,Mα] in the total Morrey spaces Lp,λ,μ(G) on any stratified Lie group G when b belongs to Lipschitz spaces Λ˙β(G). Some new characterizations for certain subclasses of Lipschitz spaces Λ˙β(G) are given. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.