Boundedness of commutators for multilinear Calderón-Zygmund operators on Generalized Morrey Spaces

Let $T$ be a $m$-linear Calderón-Zygmund operator of type $\omega$ with $\omega$ being nondecreasing and $\omega \in$ Dini(1) and $[\vec{b},T]$ be the commutator generated by $T$ with symbols $\vec{b}=(b_1,\dots ,b_m)$ belonging to generalized Campanato spaces. We give necessary and sufficient conditions for the boundedness of $[\vec{b},T]$ on generalized Morrey spaces with variable growth condition.