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 $M_{b}$, the commutators of the maximal operator $[b, M]$ and the commutators of the sharp maximal operator $[b, M^{\sharp}]$ in Orlicz spaces $L^Φ(\mathbb{G})$ on any stratified Lie group $\mathbb{G}$ when $b$ belongs to Lipschitz spaces $\dotΛ_β(\mathbb{G})$. We obtain some new characterizations for certain subclasses of Lipschitz spaces $\dotΛ_β(\mathbb{G})$.

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