Characterizations of commutators of the maximal function in total Morrey spaces on stratified Lie groups

The aim of this paper is to study the maximal commutators Mb and the commutators of the maximal operator [b, M] 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.